cp's OEIS Frontend

A383566 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 (1,0),(0,1),(4,4).

%I A383566 #10 Apr 30 2025 09:12:30
%S A383566 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,1,6,15,20,15,6,1,1,7,21,
%T A383566 35,35,21,7,1,1,8,28,56,71,56,28,8,1,1,9,36,84,128,128,84,36,9,1,1,10,
%U A383566 45,120,213,258,213,120,45,10,1,1,11,55,165,334,474,474,334,165,55,11,1
%N A383566 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 (1,0),(0,1),(4,4).
%F A383566 A(n,k) = A(k,n).
%F A383566 A(n,k) = A(n-1,k) + A(n,k-1) + A(n-4,k-4).
%F A383566 G.f.: 1 / (1 - x - y - x^4*y^4).
%e A383566 Square array A(n,k) begins:
%e A383566   1, 1,  1,  1,   1,   1,   1, ...
%e A383566   1, 2,  3,  4,   5,   6,   7, ...
%e A383566   1, 3,  6, 10,  15,  21,  28, ...
%e A383566   1, 4, 10, 20,  35,  56,  84, ...
%e A383566   1, 5, 15, 35,  71, 128, 213, ...
%e A383566   1, 6, 21, 56, 128, 258, 474, ...
%e A383566   1, 7, 28, 84, 213, 474, 954, ...
%o A383566 (PARI) a(n, k) = my(x='x+O('x^(n+1)), y='y+O('y^(k+1))); polcoef(polcoef(1/(1-x-y-x^4*y^4), n), k);
%Y A383566 Main diagonal gives A376792.
%Y A383566 Cf. A008288, A383551, A383552.
%K A383566 nonn,tabl
%O A383566 0,5
%A A383566 _Seiichi Manyama_, Apr 30 2025