OFFSET
0,2
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).
FORMULA
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)
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 *)
PROG
(PARI) a(n)=2*n*(5*n-3) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jan 02 2009
STATUS
approved