A016886 a(n) = (5*n + 3)^2.

9, 64, 169, 324, 529, 784, 1089, 1444, 1849, 2304, 2809, 3364, 3969, 4624, 5329, 6084, 6889, 7744, 8649, 9604, 10609, 11664, 12769, 13924, 15129, 16384, 17689, 19044, 20449, 21904, 23409, 24964, 26569, 28224, 29929, 31684, 33489, 35344, 37249, 39204, 41209

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's MathWorld, Polygamma Function.

Wikipedia, Polygamma Function.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, Mar 29 2017: (Start)

G.f.: (9 + x)*(1 + 4*x) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.

(End)

a(n) = A000290(A016885(n)). - Michel Marcus, Mar 30 2017

Sum_{n>=0} 1/a(n) = polygamma(1, 3/5)/25. - Amiram Eldar, Oct 02 2020

Example

a(0) = (5*0 + 3)^2 = 9.

Mathematica

(5*Range[0, 40]+3)^2 (* or *) LinearRecurrence[{3, -3, 1}, {9, 64, 169}, 40] (* Harvey P. Dale, Dec 09 2016 *)
CoefficientList[Series[(9 + x) (1 + 4 x)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, Mar 29 2017 *)

Prog

(PARI) Vec((9 + x)*(1 + 4*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Mar 29 2017
(Magma) [(5*n + 3)^2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 02 2021

Crossrefs

Cf. A000290, A016885.

Sequence in context: A165447 A050792 A171671 * A099761 A018201 A181888

Adjacent sequences: A016883 A016884 A016885 * A016887 A016888 A016889

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved