A152760 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).

0, 4, 36, 96, 184, 300, 444, 616, 816, 1044, 1300, 1584, 1896, 2236, 2604, 3000, 3424, 3876, 4356, 4864, 5400, 5964, 6556, 7176, 7824, 8500, 9204, 9936, 10696, 11484, 12300, 13144, 14016, 14916, 15844, 16800, 17784, 18796, 19836, 20904, 22000, 23124

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 4, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. The square spiral is related to the primitive Pythagorean triple [3, 4, 5]. - Omar E. Pol, Oct 13 2011

Links

Table of n, a(n) for n=0..41.

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

Formula

a(n) = 14n^2 - 10n = A001106(n)*4 = A139268(n)*2.

a(n) = a(n-1) + 28*n - 24 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010

From Colin Barker, Apr 09 2012: (Start)

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

G.f.: 4*x*(1+6*x)/(1-x)^3. (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 4, 8!, 28}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
4*PolygonalNumber[9, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3, -3, 1}, {0, 4, 36}, 50] (* Harvey P. Dale, Aug 26 2019 *)

Prog

(PARI) a(n)=2*n*(7*n-5) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A001106, A139268, A152759.

Sequence in context: A075215 A193833 A193183 * A361719 A016826 A190318

Adjacent sequences: A152757 A152758 A152759 * A152761 A152762 A152763

Keyword

easy,nonn

Author

Omar E. Pol, Dec 14 2008

Status

approved