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 A383567 #11 Apr 30 2025 09:14:06
%S A383567 1,0,0,1,0,1,0,0,0,0,1,0,2,0,1,0,0,0,0,0,0,1,0,3,0,3,0,1,0,0,0,0,0,0,
%T A383567 0,0,1,0,4,0,6,0,4,0,1,0,0,0,0,0,0,0,0,0,0,1,0,5,0,10,1,10,0,5,0,1,0,
%U A383567 0,0,0,0,0,0,0,0,0,0,0,1,0,6,0,15,2,20,2,15,0,6,0,1
%N A383567 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (2,0),(0,2),(5,5).
%F A383567 A(n,k) = A(k,n).
%F A383567 If n - k == 1 (mod 2), A(n,k) = 0.
%F A383567 A(n,k) = A(n-2,k) + A(n,k-2) + A(n-5,k-5).
%F A383567 G.f.: 1 / (1 - x^2 - y^2 - x^5*y^5).
%e A383567 Square array A(n,k) begins:
%e A383567 1, 0, 1, 0, 1, 0, 1, 0, 1, ...
%e A383567 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e A383567 1, 0, 2, 0, 3, 0, 4, 0, 5, ...
%e A383567 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e A383567 1, 0, 3, 0, 6, 0, 10, 0, 15, ...
%e A383567 0, 0, 0, 0, 0, 1, 0, 2, 0, ...
%e A383567 1, 0, 4, 0, 10, 0, 20, 0, 35, ...
%e A383567 0, 0, 0, 0, 0, 2, 0, 6, 0, ...
%e A383567 1, 0, 5, 0, 15, 0, 35, 0, 70, ...
%o A383567 (PARI) a(n, k) = my(x='x+O('x^(n+1)), y='y+O('y^(k+1))); polcoef(polcoef(1/(1-x^2-y^2-x^5*y^5), n), k);
%Y A383567 Main diagonal gives A383568.
%Y A383567 Cf. A027907, A383550.
%K A383567 nonn,tabl
%O A383567 0,13
%A A383567 _Seiichi Manyama_, Apr 30 2025