A153808 8 times octagonal numbers: 8*n*(3*n-2).

0, 8, 64, 168, 320, 520, 768, 1064, 1408, 1800, 2240, 2728, 3264, 3848, 4480, 5160, 5888, 6664, 7488, 8360, 9280, 10248, 11264, 12328, 13440, 14600, 15808, 17064, 18368, 19720, 21120, 22568, 24064, 25608, 27200, 28840, 30528, 32264

Offset: 0

Author

Omar E. Pol, Jan 19 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..999
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000567 (octagonal numbers), A064201 (9 times octagonal numbers), A139267 (twice octagonal numbers), A152751 (3 times octagonal numbers), A153794 (4 times octagonal numbers).

Programs

Magma

[ 8*n*(3*n-2): n in [0..40] ];

Mathematica

Table[8*n*(3*n-2), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,8,64}, 25] (* G. C. Greubel, Aug 29 2016 *)
8*PolygonalNumber[8,Range[0,40]] (* Harvey P. Dale, Nov 22 2023 *)

PARI

a(n)=24*n^2-16*n \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 24*n^2 - 16*n = 8*A000567(n) = 4*A139267(n) = 2*A153794(n).

a(n) = a(n-1) + 48*n - 40 (with a(0)=0). - Vincenzo Librandi, Nov 27 2010

From G. C. Greubel, Aug 29 2016: (Start)

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

G.f.: 8*x*(1 + 5*x)/(1 - x)^3.

E.g.f.: 8*x*(1 + 3*x)*exp(x). (End)