I am trying to recreate the following image in TikZ

Using some old code I was able to produce the following result

While I was able to produce the correct result, I feel that my solution was a bit strange as it required two passes. Any suggestions for alternative approaches, or improvements to the code are more than welcome.

documentclass[tikz]standalone

begindocument

begintikzpicture[x=1cm]
edefsize4
 foreach x in 0,...,size foreach y in 0,...,size
 
 pgfmathparsemod(x+y,size) ? "none" : "black"
 edefcolourpgfmathresult
 path[draw=black, fill=colour] (x,y) rectangle ++ (1,1);

 pgfmathparsex==y ? "black" : "none"
 edefcolourpgfmathresult
 path[fill=colour] (x,y) rectangle ++ (1,1);
 
 draw (0,0)--(0,size+1)--(size+1,size+1)--(size+1,0)--cycle;
endtikzpicture

enddocument

With tikz:

documentclass[tikz]standalone

begindocument
 begintikzpicture[
node distance = 0mm,
 box/.style = draw, minimum size=10mm, fill=black,
 outer sep=0pt,
 ]
edefsize4
foreach y in 0,...,size
foreach x in 0,...,size
ifnumx=y
node[box] at (x,size-y) ;
node[box] at (x,y) ;
 else
node[box,fill=none] at (x,y) ;
 fi

 endtikzpicture
enddocument

Note: Value of size had to be zero or any even natural number (0, 2, 4, ...)

addendum:

• default baseline of above image is as (current bounding box.south)˙ For series of those images for different value ofsize` is:

documentclassarticle
usepackagetikz
usepackagetabularx
newcolumntypeC>centeringarraybackslashX

begindocument
 beginfigure
begintabularxlinewidth>hsize=0.5hsizeC C >hsize=1.5hsizeC
 begintikzpicture[baseline=(current bounding box.south),
node distance = 0mm,
 box/.style = draw, minimum size=10mm, fill=black,
 outer sep=0pt,
 ]
edefsize0 % in this MWE the meaning of `size` is changed
foreach y in 0,...,size
foreach x in 0,...,size
ifnumx=y
node[box] at (x,size-y) ;
node[box] at (x,y) ;
 else
node[box,fill=none] at (x,y) ;
 fi

 endtikzpicture
 caption
&
 begintikzpicture[%baseline=(current bounding box.south),
node distance = 0mm,
 box/.style = draw, minimum size=10mm, fill=black,
 outer sep=0pt,
 ]
edefsize1
foreach y in 0,...,2*size % changed, now number of boxes is odd 
foreach x in 0,...,2*size % changed,
ifnumx=y
node[box] at (x,size-y) ;
node[box] at (x,y) ;
 else
node[box,fill=none] at (x,y) ;
 fi

 endtikzpicture
 caption
&
 begintikzpicture[baseline=(current bounding box.south),
node distance = 0mm,
 box/.style = draw, minimum size=10mm, fill=black,
 outer sep=0pt,
 ]
edefsize2
foreach y in 0,...,size
foreach x in 0,...,size
ifnumx=y
node[box] at (x,size-y) ;
node[box] at (x,y) ;
 else
node[box,fill=none] at (x,y) ;
 fi

 endtikzpicture
 caption
endtabularx
 endfigure
enddocument

A PSTricks solution only for fun purposes!

documentclass[border=1pt]standalone
usepackagepstricks
defobj#1%
 pspicture[dimen=m](#1,#1)
 multips(0,0)(0,1)#1multips(0,0)(1,0)#1psframe(1,1)
 multips(0,0)(1,1)#1psframe*(1,1)
 multips(0,#1)(1,-1)#1psframe*(1,-1)
 endpspicture

begindocument
foreach i in 3,5,7objiquad
enddocument

Edit

I invented the algorithm (that has not been patented yet) as follows. No nested loop is needed.

documentclass[border=12pt]standalone
usepackage[nomessages]fp
usepackagexintexpr
usepackagepstricks
pssetunit=5mm
defobj#1%
 pspicture[dimen=m](#1,#1)
 FPevalN#1*#1-1
 foreach j in 0,...,N
 
 FPevalytrunc(j/#1:0)
 FPevalxj-#1*y
 xintifboolexpr
 psframe[fillstyle=solid,fillcolor=black](x,y)(+x+1,y+1)
 psframe(x,y)(+x+1,y+1)
 
 endpspicture
begindocument
foreach i in 1,3,5,7,9objiquad
enddocument

Edit:
The following works for all values of size

documentclass[tikz]standalone

begindocument

begintikzpicture
edefsize4
 foreach x in 0,...,size foreach y in 0,...,size 
 pgfmathsetmacrocolour(x==y 
 draw[fill=colour] (x,y) rectangle ++ (1,1);
 
endtikzpicture

enddocument

I do not see the reason for a double loop, nor complicated conditions.

documentclass[tikz,border=3.14mm]standalone
begindocument
begintikzpicture[xboard/.style=insert path=
(0,0) grid (#1,#1)
foreach X in 1,...,#1
(X-0.5,X-0.5) picbx (X-0.5,#1-X+0.5) picbx,
pics/bx/.style=code=fill (-0.5,-0.5) rectangle (0.5,0.5);]
draw[xboard=1] [xshift=2cm,xboard=3]
[xshift=4cm,xboard=5] [xshift=6cm,xboard=7];
endtikzpicture
enddocument