A153784 4 times heptagonal numbers: a(n) = 2*n*(5*n-3).

0, 4, 28, 72, 136, 220, 324, 448, 592, 756, 940, 1144, 1368, 1612, 1876, 2160, 2464, 2788, 3132, 3496, 3880, 4284, 4708, 5152, 5616, 6100, 6604, 7128, 7672, 8236, 8820, 9424, 10048, 10692, 11356, 12040, 12744, 13468, 14212, 14976, 15760, 16564, 17388, 18232, 19096

Offset: 0

Author

Omar E. Pol, Jan 02 2009

Keywords

• easy
• nonn

Comments

Sequence found by reading the line from 0, in the direction 0, 4, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012

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. A000566, A085787, A087348, A135706, A152745, A152773.

Programs

Mathematica

s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,4,6!,20}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
Table[2n(5n-3),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,4,28},50] (* Harvey P. Dale, Mar 19 2015 *)

PARI

a(n)=2*n*(5*n-3) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 10*n^2 - 6*n = 4*A000566(n) = 2*A135706(n).

a(n) = 20*n + a(n-1) - 16 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(n) = A087348(n) - 1, n >= 1. - Omar E. Pol, Jul 18 2012

a(0)=0, a(1)=4, a(2)=28, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 19 2015

From Elmo R. Oliveira, Dec 15 2024: (Start)

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

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

a(n) = A152745(n) - n. (End)