A153780 10 times pentagonal numbers: a(n) = 5*n*(3*n-1).

0, 10, 50, 120, 220, 350, 510, 700, 920, 1170, 1450, 1760, 2100, 2470, 2870, 3300, 3760, 4250, 4770, 5320, 5900, 6510, 7150, 7820, 8520, 9250, 10010, 10800, 11620, 12470, 13350, 14260, 15200, 16170, 17170, 18200, 19260, 20350

Offset: 0

Author

Omar E. Pol, Jan 01 2009

Keywords

• nonn
• easy

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. A000326, A049450, A152734, A152996, A153449.

Programs

Mathematica

Table[5*n*(3*n - 1), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,10,50},25] (* G. C. Greubel, Aug 28 2016 *)

PARI

a(n) = 5*n*(3*n-1); \\ Michel Marcus, Aug 28 2016

Formula

a(n) = 15*n^2 - 5*n = 10*A000326(n) = 5*A049450(n) = 2*A152734(n).

a(n) = 30*n + a(n-1) - 20 for n>0, a(0) = 0. - Vincenzo Librandi, Aug 03 2010

G.f.: 10*x*(1+2*x)/(1-x)^3. - Colin Barker, Feb 14 2012

From G. C. Greubel, Aug 28 2016: (Start)

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

E.g.f.: 5*x*(2 + 3*x)*exp(x). (End)