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 A125226 #9 May 11 2025 22:05:58 %S A125226 1,1,1,0,1,0,0,2,2,0,0,1,4,1,0,0,0,4,4,0,0,0,0,3,9,3,0,0,0,0,1,11,11, %T A125226 1,0,0,0,0,0,8,21,8,0,0,0,0,0,0,4,27,27,4,0,0,0,0,0,0,1,23,52,23,1,0, %U A125226 0,0,0,0,0,0,13,67,67,13,0,0,0,0,0,0,0,0,5,62,127,62,5,0,0,0,0,0,0,0,0,1,41 %N A125226 Array, read by antidiagonals, where A(1,1) = A(1,2) = A(2,1) = A(2,2) = 1, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1). %C A125226 It appears that the main diagonal (1,1,4,9,21,...) is A051292 (Whitney number of level n of the lattice of the ideals of the crown of size 2 n). It appears that if b(n) = the n-th antidiagonal sum - A108014(n-1) then the sequence b(n) is the sequence 1,0,-2,0,1,0 repeated. n-th row sum = A052945(n). %F A125226 A(1,1) = A(1,2) = A(2,1) = A(2,2) = 1, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1) %e A125226 Array begins: %e A125226 1 1 0 0 0 0 0 ... %e A125226 1 1 2 1 0 0 0 ... %e A125226 0 2 4 4 3 1 0 ... %e A125226 ... %o A125226 (PARI) A=matrix(22,22);A[1,1]=1;A[1,2]=1;A[2,1]=1;A[2,2]=1;A[3,2]=2;A[2,3]=2;A[2,4]=1;A[4,2]=1; for(n=3,22,for(k=3,22,A[n,k]=A[n-2,k-2]+A[n-1,k-2]+A[n-2,k-1]+A[n-1,k-1])); for(n=1,22,for(i=1,n,print1(A[n-i+1,i],", "))) %Y A125226 Cf. A051292, A052945, A108014. %K A125226 nonn,tabl %O A125226 1,8 %A A125226 _Gerald McGarvey_, Jan 14 2007