A153797 7 times octagonal numbers: a(n) = 7*n*(3*n-2).

0, 7, 56, 147, 280, 455, 672, 931, 1232, 1575, 1960, 2387, 2856, 3367, 3920, 4515, 5152, 5831, 6552, 7315, 8120, 8967, 9856, 10787, 11760, 12775, 13832, 14931, 16072, 17255, 18480, 19747, 21056, 22407, 23800, 25235, 26712, 28231

Offset

0,2

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) = 21*n^2 - 14*n = 7*A000567(n).

a(n) = a(n-1) + 42*n - 35 (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.: 7*x*(1 + 5*x)/(1 - x)^3.

E.g.f.: 7*x*(1 + 3*x)*exp(x). (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 7, 8!, 42}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[7*n*(3*n-2), {n, 0, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 56}, 25] (* G. C. Greubel, Aug 29 2016 *)

Prog

(Magma) [ 7*n*(3*n-2): n in [0..40] ];
(PARI) a(n)=7*n*(3*n-2) \\ Charles R Greathouse IV, Aug 29 2016

Crossrefs

Cf. A000567 (octagonal numbers), A153796, A153808.

Sequence in context: A097254 A043911 A044526 * A244727 A090224 A237647

Adjacent sequences: A153794 A153795 A153796 * A153798 A153799 A153800

Keyword

easy,nonn

Author

Omar E. Pol, Jan 20 2009

Status

approved