A247155 a(n) = 31*n^2 + 1.

1, 32, 125, 280, 497, 776, 1117, 1520, 1985, 2512, 3101, 3752, 4465, 5240, 6077, 6976, 7937, 8960, 10045, 11192, 12401, 13672, 15005, 16400, 17857, 19376, 20957, 22600, 24305, 26072, 27901, 29792, 31745, 33760, 35837, 37976, 40177, 42440, 44765, 47152, 49601

Offset

0,2

Links

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

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

Formula

a(0)=1, a(1)=32, a(2)=125, a(3)=280, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 28 2016

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: (32*x^2+29*x+1)/(1-x)^3.

E.g.f.: exp(x)*(1 + 31*x + 31*x^2).

a(n) = A010020(n) - 1 for n>=1. (End)

Mathematica

31*Range[100]^2+1 (* or *) LinearRecurrence[{3, -3, 1}, {32, 125, 280}, 100] (* Harvey P. Dale, Apr 28 2016 *)

Prog

(PARI) a(n)=31*n^2+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A010020.

Sequence in context: A344219 A271532 A264480 * A239728 A244082 A033323

Adjacent sequences: A247152 A247153 A247154 * A247156 A247157 A247158

Keyword

nonn,easy

Author

Garrett Backer, Nov 21 2014

Status

approved