A367653 G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2 + x^3) * A(x^4)).

1, 1, 2, 4, 8, 16, 32, 64, 128, 257, 515, 1032, 2068, 4146, 8310, 16656, 33384, 66916, 134125, 268837, 538850, 1080064, 2164860, 4339204, 8697416, 17432944, 34942268, 70037629, 140382111, 281379296, 563991416, 1130453878, 2265860666, 4541648896, 9103196384

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} a(floor(k/4)) * a(n-1-k).

Mathematica

terms = 35; A[_] = 0; Do[A[x_] = 1/(1-x*(1+x+x^2+x^3)*A[x^4])+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Nov 15 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, v[j\4+1]*v[i-j])); v;

Crossrefs

Cf. A127680, A367652, A367654.

Cf. A367660.

Sequence in context: A275075 A275063 A186026 * A023423 A210544 A395145

Adjacent sequences: A367650 A367651 A367652 * A367654 A367655 A367656

Keyword

nonn

Author

Seiichi Manyama, Nov 26 2023

Status

approved