OFFSET
1,2
LINKS
Ivan Panchenko, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Centered Polygonal Numbers.
R. Yin, J. Mu, and T. Komatsu, The p-Frobenius Number for the Triple of the Generalized Star Numbers, Preprints 2024, 2024072280. See p. 2.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 11*n^2 - 11*n + 1.
a(n) = 22*n + a(n-1) - 22 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010
From Amiram Eldar, Jun 21 2020: (Start)
Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7/11)*Pi/2)/sqrt(77).
Sum_{n>=1} a(n)/n! = 12*e - 1.
Sum_{n>=1} (-1)^n * a(n)/n! = 12/e - 1. (End)
E.g.f.: exp(x)*(1 + 11 * x^2) - 1. - Nikolaos Pantelidis, Feb 06 2023
From Elmo R. Oliveira, Oct 22 2024: (Start)
G.f.: x*(1 + 20*x + x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
EXAMPLE
a(5) = 221 because 11*5^2 - 11*5 + 1 = 275 - 55 + 1 = 221
For n=2, a(2)=22*2+1-22=23; n=3, a(3)=22*3+23-22=67; n=4, a(4)=22*4+67-22=133.
MATHEMATICA
FoldList[#1 + #2 &, 1, 22 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
PROG
(PARI) a(n)=11*n^2-11*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Terrel Trotter, Jr., Apr 09 2002
STATUS
approved