A391600 a(n) = Sum_{k=0..floor((2*n+1)/3)} binomial(2*k+1,2*n-3*k+1).

1, 1, 3, 5, 11, 22, 44, 92, 181, 379, 750, 1557, 3109, 6401, 12872, 26349, 53228, 108575, 219918, 447702, 908140, 1846804, 3749001, 7619870, 15474230, 31443013, 63865592, 129755543, 263576791, 535475968, 1087774536, 2209835169, 4489176073, 9119740067

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,1,-2,1).

Formula

G.f.: (1 + x - x^2) / (1 - 4*x^2 - x^3*(1-x)^2).

a(n) = 4*a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

Mathematica

LinearRecurrence[{0, 4, 1, -2, 1}, {1, 1, 3, 5, 11}, 50] (* Vincenzo Librandi, Jan 14 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1+x-x^2)/(1-4*x^2-x^3*(1-x)^2))
(Magma) I:=[1, 1, 3, 5, 11]; [n le 5 select I[n] else 4*Self(n-2) + Self(n-3) - 2*Self(n-4) + Self(n-5): n in [1..40]]; // Vincenzo Librandi, Jan 14 2026

Crossrefs

Cf. A376726, A392487, A376727, A392488, A376728.

Cf. A392454.

Sequence in context: A341532 A293338 A168655 * A394221 A005830 A007008

Adjacent sequences: A391597 A391598 A391599 * A391601 A391602 A391603

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved