A153793 13 times pentagonal numbers: a(n) = 13*n*(3*n-1)/2.

0, 13, 65, 156, 286, 455, 663, 910, 1196, 1521, 1885, 2288, 2730, 3211, 3731, 4290, 4888, 5525, 6201, 6916, 7670, 8463, 9295, 10166, 11076, 12025, 13013, 14040, 15106, 16211, 17355, 18538, 19760, 21021, 22321, 23660, 25038, 26455

Offset: 0

Author

Omar E. Pol, Jan 01 2009

Keywords

• nonn
• easy

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000326, A153792.

Programs

Magma

[13*n*(3*n-1)/2: n in [0..60]]; // Wesley Ivan Hurt, Aug 29 2016

Maple

A153793:=n->13*n*(3*n-1)/2: seq(A153793(n), n=0..60); # Wesley Ivan Hurt, Aug 29 2016

Mathematica

Table[13*n*(3*n-1)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,13,65}, 25] (* G. C. Greubel, Aug 29 2016 *)
13*PolygonalNumber[5,Range[0,40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 16 2016 *)

PARI

a(n) = (39*n^2 - 13*n)/2; \\ Altug Alkan, Aug 29 2016

Formula

a(n) = (39*n^2 - 13*n)/2 = 13*A000326(n).

a(n) = 39*n + a(n-1) - 26 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

G.f.: 13*x*(1 + 2*x)/(1-x)^3. - Colin Barker, Feb 14 2012

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

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

E.g.f.: (13/2)*x*(2+3*x)*exp(x). (End)