A158056 a(n) = 16*n^2 + 2*n.

18, 68, 150, 264, 410, 588, 798, 1040, 1314, 1620, 1958, 2328, 2730, 3164, 3630, 4128, 4658, 5220, 5814, 6440, 7098, 7788, 8510, 9264, 10050, 10868, 11718, 12600, 13514, 14460, 15438, 16448, 17490, 18564, 19670, 20808, 21978, 23180, 24414, 25680

Offset: 1

Author

Vincenzo Librandi, Mar 12 2009

Keywords

• nonn
• easy

Comments

The identity (16*n + 1)^2 - (16*n^2 + 2*n)*4^2 = 1 can be written as A158057(n)^2 - a(n)*4^2 = 1. - Vincenzo Librandi, Feb 09 2012

Sequence found by reading the line from 18, in the direction 18, 68, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A158057.

Programs

Magma

I:=[18, 68, 150]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

Mathematica

LinearRecurrence[{3,-3,1},{18,68,150},50]
Table[16n^2+2n,{n,40}]  (* Harvey P. Dale, Apr 13 2011 *)

PARI

a(n) = 16*n^2 + 2*n.

Formula

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

G.f.: 2*x*(-9 - 7*x)/(x-1)^3.