A377663 a(n) = 2*n^3 - 3*n + 1.

1, 0, 11, 46, 117, 236, 415, 666, 1001, 1432, 1971, 2630, 3421, 4356, 5447, 6706, 8145, 9776, 11611, 13662, 15941, 18460, 21231, 24266, 27577, 31176, 35075, 39286, 43821, 48692, 53911, 59490, 65441, 71776, 78507, 85646, 93205, 101196, 109631, 118522, 127881, 137720

Offset

0,3

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = [x^n] (-2*x^3 + 17*x^2 - 4*x + 1)/(x - 1)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3. - Chai Wah Wu, Nov 14 2024

From Elmo R. Oliveira, Jul 04 2026: (Start)

a(n) = 1 + A163322(n)/4.

E.g.f.: exp(x)*(1 - x + 6*x^2 + 2*x^3). (End)

Maple

a := n -> 2*n^3 - 3*n + 1: seq(a(n), n = 0..41);

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 0, 11, 46}, 42] (* James C. McMahon, Nov 14 2024 *)

Prog

(Magma) [2*n^3 - 3*n + 1 : n in [0..60]]; // Wesley Ivan Hurt, Aug 05 2025

Crossrefs

Column 3 of A377666.

Cf. A163322.

Sequence in context: A063158 A396288 A081587 * A223834 A359096 A143059

Adjacent sequences: A377660 A377661 A377662 * A377664 A377665 A377666

Keyword

nonn,easy,changed

Author

Peter Luschny, Nov 14 2024

Status

approved