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URL: https://oeis.org/A069178

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A069178
Centered 21-gonal numbers.
6
1, 22, 64, 127, 211, 316, 442, 589, 757, 946, 1156, 1387, 1639, 1912, 2206, 2521, 2857, 3214, 3592, 3991, 4411, 4852, 5314, 5797, 6301, 6826, 7372, 7939, 8527, 9136, 9766, 10417, 11089, 11782, 12496, 13231, 13987, 14764, 15562, 16381, 17221, 18082, 18964
OFFSET
1,2
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 51.
FORMULA
a(n) = (21*n^2 - 21*n + 2)/2.
a(n) = 21*n + a(n-1) - 21 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010
G.f. -x*(1+19*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011
Binomial transform of [1, 21, 21, 0, 0, 0, ...] and Narayana transform (A001263) of [1, 21, 0, 0, 0, ...]. - Gary W. Adamson, Jul 26 2011
a(n) = 1 + Sum_{i=1..n} 21*(i-1). - Wesley Ivan Hurt, May 25 2013
From Amiram Eldar, Jun 21 2020: (Start)
Sum_{n>=1} 1/a(n) = 2*Pi*tan(sqrt(13/21)*Pi/2)/sqrt(273).
Sum_{n>=1} a(n)/n! = 23*e/2 - 1.
Sum_{n>=1} (-1)^n * a(n)/n! = 23/(2*e) - 1. (End)
E.g.f.: exp(x)*(1 + 21*x^2/2)-1. - Nikolaos Pantelidis, Feb 06 2023
MATHEMATICA
FoldList[#1 + #2 &, 1, 21 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
LinearRecurrence[{3, -3, 1}, {1, 22, 64}, 60] (* Harvey P. Dale, Jun 13 2022 *)
PROG
(PARI) a(n)=(21*n^2-21*n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Cf. centered polygonal numbers listed in A069190.
Sequence in context: A221595 A051874 A140390 * A081929 A305064 A124715
KEYWORD
easy,nonn
AUTHOR
Terrel Trotter, Jr., Apr 09 2002
STATUS
approved