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 A376791 #17 Apr 30 2025 09:13:15
%S A376791 1,2,6,21,76,282,1065,4074,15732,61193,239406,941064,3713701,14703896,
%T A376791 58383138,232383841,926943678,3704410890,14828984641,59450138412,
%U A376791 238659074286,959247218253,3859777477944,15546444564846,62675854384977,252893414725842,1021208266423260
%N A376791 Expansion of 1/sqrt((1 - x^3)^2 - 4*x).
%C A376791 From _Seiichi Manyama_, Apr 30 2025: (Start)
%C A376791 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(0,1),(3,3).
%C A376791 Diagonal of the rational function 1 / (1 - x - y - x^3*y^3). (End)
%F A376791 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k) * binomial(2*n-6*k,n-3*k).
%o A376791 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x^3)^2-4*x))
%o A376791 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k, k)*binomial(2*n-6*k, n-3*k));
%Y A376791 Cf. A001850, A349713, A376792.
%Y A376791 Cf. A053442, A098479.
%K A376791 nonn
%O A376791 0,2
%A A376791 _Seiichi Manyama_, Oct 04 2024