This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384759 #17 Jun 26 2025 01:25:33
%S A384759 0,3,2031,728174,247646098,91880342535,38818192375310,
%T A384759 18907485764545412,10626953883068264472,6866760686250915376779,
%U A384759 5073038373153476636807709,4259014676256866422905669602,4038463837000965678262091166880,4299625631242136963071149921577615,5111407212497576694797045579672852791
%N A384759 Number of legal arrangements in pawn-only chess on an n X n board where no pieces have been taken and no piece attacks another piece.
%C A384759 The number of ways of arranging n pawns of each color on an n X n board such that no pawn threatens another, each file contains one pawn of each color, none of the pawns are passed pawns, and each pawn is placed between row 2 and row n-1 inclusive.
%C A384759 There is no requirement that the arrangements counted here can actually be achieved via a sequence of legal chess moves.
%e A384759 The a(5) = 3 positions are:
%e A384759 . . . . . . . . . . . . . . .
%e A384759 b b b b b . b . b . b . b . b
%e A384759 . . . . . b w b w b w b w b w
%e A384759 w w w w w w . w . w . w . w .
%e A384759 . . . . . . . . . . . . . . .
%o A384759 (PARI)
%o A384759 MkTfrMtx(n)={my(m=binomial(n,2), M=matrix(m,m)); for(i=1,n-1, for(j=i+1,n, for(p=1,n-1, for(q=p+1,n, if(q<>i+1&&j<>p+1, M[binomial(n-i,2)+(j-i), binomial(n-p,2)+(q-p)]=1) )))); M}
%o A384759 a(n)={my(M=MkTfrMtx(n-2)); vecsum(M^(n-1)*vectorv(#M,i,1))} \\ _Andrew Howroyd_, Jun 15 2025
%Y A384759 Cf. A035290, A294240.
%K A384759 nonn
%O A384759 4,2
%A A384759 _Edwin Hermann_, Jun 09 2025
%E A384759 a(9) onwards from _Andrew Howroyd_, Jun 15 2025