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A069173
Centered 22-gonal numbers.
7
1, 23, 67, 133, 221, 331, 463, 617, 793, 991, 1211, 1453, 1717, 2003, 2311, 2641, 2993, 3367, 3763, 4181, 4621, 5083, 5567, 6073, 6601, 7151, 7723, 8317, 8933, 9571, 10231, 10913, 11617, 12343, 13091, 13861, 14653, 15467, 16303, 17161, 18041, 18943, 19867, 20813
OFFSET
1,2
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
Cf. centered polygonal numbers listed in A069190.
Sequence in context: A053559 A322414 A031376 * A124716 A139955 A126377
KEYWORD
easy,nonn
AUTHOR
Terrel Trotter, Jr., Apr 09 2002
STATUS
approved