A323218 a(n) = (4*n^3 + 30*n^2 + 50*n)/3 + 1.

1, 29, 85, 177, 313, 501, 749, 1065, 1457, 1933, 2501, 3169, 3945, 4837, 5853, 7001, 8289, 9725, 11317, 13073, 15001, 17109, 19405, 21897, 24593, 27501, 30629, 33985, 37577, 41413, 45501, 49849, 54465, 59357, 64533, 70001, 75769, 81845, 88237, 94953, 102001

Offset

0,2

Links

Table of n, a(n) for n=0..40.

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

Formula

From Elmo R. Oliveira, May 21 2026: (Start)

G.f.: (1 + 25*x - 25*x^2 + 7*x^3)/(1 - x)^4.

E.g.f.: (1/3)*(3 + 84*x + 42*x^2 + 4*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Maple

a := n -> (4*n^3 + 30*n^2 + 50*n)/3 + 1: seq(a(n), n = 0..40);

Mathematica

Table[(4n^3+30n^2+50n)/3+1, {n, 0, 40}] (* Harvey P. Dale, May 24 2019 *)

Crossrefs

Column 4 of A323222.

Sequence in context: A255187 A273362 A195314 * A124784 A126383 A032508

Adjacent sequences: A323215 A323216 A323217 * A323219 A323220 A323221

Keyword

nonn,easy

Author

Peter Luschny, Jan 26 2019

Status

approved