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

0,2

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).

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)

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 *)

Prog

(Magma) [ 8*n*(3*n-2): n in [0..40] ];
(PARI) a(n)=24*n^2-16*n \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

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

Sequence in context: A255932 A043152 A044195 * A207601 A207027 A207172

Adjacent sequences: A153805 A153806 A153807 * A153809 A153810 A153811

Keyword

easy,nonn

Author

Omar E. Pol, Jan 19 2009

Status

approved