A153794 4 times octagonal numbers: a(n) = 4*n*(3*n-2).

0, 4, 32, 84, 160, 260, 384, 532, 704, 900, 1120, 1364, 1632, 1924, 2240, 2580, 2944, 3332, 3744, 4180, 4640, 5124, 5632, 6164, 6720, 7300, 7904, 8532, 9184, 9860, 10560, 11284, 12032, 12804, 13600, 14420, 15264, 16132, 17024

Offset

0,2

Comments

Sequence found by reading the segment (0, 4) together with the line from 4, in the direction 4, 32, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Jul 18 2012

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 12*n^2 - 8*n = 4*A000567(n) = 2*A139267(n).

a(n) = 24*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=4, a(2)=32, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jul 14 2011

G.f.: 4*(x + 5*x^2)/(1-x)^3. - Harvey P. Dale, Jul 14 2011

E.g.f.: 4*x*(1 + 3*x)*exp(x). - G. C. Greubel, Aug 29 2016

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 4, 7!, 24}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
Table[4n(3n-2), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 4, 32}, 41] (* Harvey P. Dale, Jul 14 2011 *)
4*PolygonalNumber[8, Range[0, 40]] (* Harvey P. Dale, Dec 04 2022 *)

Prog

(PARI) a(n) = 12*n^2 - 8*n; \\ Altug Alkan, Aug 29 2016

Crossrefs

Cf. A000567, A139267, A152751, A153808.

Sequence in context: A113250 A329910 A012036 * A222326 A370082 A108914

Adjacent sequences: A153791 A153792 A153793 * A153795 A153796 A153797

Keyword

easy,nonn

Author

Omar E. Pol, Jan 19 2009

Status

approved