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

Author

Klaus Brockhaus, Jan 04 2009

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

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

Programs

Magma

[ 12*n^2+22*n+11: n in [0..39] ];

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 *)

PARI

a(n)=12*n^2+22*n+11 \\ Charles R Greathouse IV, Oct 16 2015

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