A082112 a(n) = 4*n^2 + 10*n + 1.

1, 15, 37, 67, 105, 151, 205, 267, 337, 415, 501, 595, 697, 807, 925, 1051, 1185, 1327, 1477, 1635, 1801, 1975, 2157, 2347, 2545, 2751, 2965, 3187, 3417, 3655, 3901, 4155, 4417, 4687, 4965, 5251, 5545, 5847, 6157, 6475, 6801, 7135, 7477, 7827, 8185, 8551

Offset

0,2

Comments

A row of number array A082110.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + 8*n + 6 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: (1+12*x-5*x^2) / (1-x)^3. - R. J. Mathar, Dec 03 2014

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Wesley Ivan Hurt, Dec 22 2021

E.g.f.: (1 + 14*x + 4*x^2)*exp(x). - G. C. Greubel, Dec 22 2022

Mathematica

Table[n +(n+1)^2 -4, {n, 1, 200, 2}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
LinearRecurrence[{3, -3, 1}, {1, 15, 37}, 50] (* Harvey P. Dale, Dec 18 2014 *)

Prog

(PARI) a(n)=4*n^2+10*n+1 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [4*n^2 + 10*n + 1 : n in [0..50]]; // Wesley Ivan Hurt, Dec 22 2021
(SageMath) [4*n^2+10*n+1 for n in range(51)] # G. C. Greubel, Dec 22 2022

Crossrefs

Cf. A082108, A082109, A082110.

Sequence in context: A260796 A296179 A181362 * A059605 A147221 A051461

Adjacent sequences: A082109 A082110 A082111 * A082113 A082114 A082115

Keyword

easy,nonn

Author

Paul Barry, Apr 04 2003

Status

approved