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

1,1

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).

Formula

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

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

Mathematica

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

Prog

(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]];
(PARI) a(n) = 16*n^2 + 2*n.

Crossrefs

Cf. A158057.

Sequence in context: A143859 A063523 A045234 * A304061 A214491 A135470

Adjacent sequences: A158053 A158054 A158055 * A158057 A158058 A158059

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 12 2009

Status

approved