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

Author

Omar E. Pol, Jan 19 2009

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000567, A139267, A152751, A153808.

Programs

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 *)

PARI

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

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