A154106 a(n) = 12*n^2 + 22*n + 11.

11, 45, 103, 185, 291, 421, 575, 753, 955, 1181, 1431, 1705, 2003, 2325, 2671, 3041, 3435, 3853, 4295, 4761, 5251, 5765, 6303, 6865, 7451, 8061, 8695, 9353, 10035, 10741, 11471, 12225, 13003, 13805, 14631, 15481, 16355, 17253, 18175, 19121

Offset

0,1

Comments

Sequence found by reading the line from 11, in the direction 11, 45,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Jul 18 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1 +x)*(11 +x)/(1-x)^3.

a(n) = 2*n*A016969(n+1) + 11.

a(0) = 11; for n > 0, a(n) = a(n-1) + 24*n + 10.

a(n) = 2 + A185918(n+1). - Omar E. Pol, Jul 18 2012

E.g.f.: (11 + 34*x + 12*x^2)*exp(x). - G. C. Greubel, Sep 02 2016

Example

a(3) = 12*3^2 + 22*3 + 11 = 185 = 2*3*29 + 11 = 2*3*A016969(4) + 11.
a(4) = a(3) +24*4 +10 = 185 +96 +10 = 291.

Mathematica

Table[12n^2+22n+11, {n, 0, 50}]  (* Harvey P. Dale, Mar 16 2011 *)
LinearRecurrence[{3, -3, 1}, {11, 45, 103}, 25] (* G. C. Greubel, Sep 02 2016 *)

Prog

(Magma) [ 12*n^2+22*n+11: n in [0..39] ];
(PARI) a(n)=12*n^2+22*n+11 \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A016969 (6n+5), A153286, A185918, A194454.

Sequence in context: A042521 A041228 A022280 * A232613 A357736 A057813

Adjacent sequences: A154103 A154104 A154105 * A154107 A154108 A154109

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 04 2009

Status

approved