A153785 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.

0, 5, 35, 90, 170, 275, 405, 560, 740, 945, 1175, 1430, 1710, 2015, 2345, 2700, 3080, 3485, 3915, 4370, 4850, 5355, 5885, 6440, 7020, 7625, 8255, 8910, 9590, 10295, 11025, 11780, 12560, 13365, 14195, 15050, 15930, 16835, 17765

Offset: 0

Author

Omar E. Pol, Jan 07 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. A000566, A153784, A154786.

Programs

Mathematica

s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,5,8!,25}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[5*n*(5*n - 3)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,5,35}, 25] (* G. C. Greubel, Aug 28 2016 *)

PARI

a(n) = 5*n*(5*n-3)/2; \\ Michel Marcus, Aug 28 2016

Formula

a(n) = (25*n^2 - 15*n)/2 = A000566(n)*5.

a(n) = 25*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

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

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

G.f.: 5*x*(1 + 4*x)/(1 - x)^3.

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