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A051875 23-gonal numbers: a(n) = n(21n-19)/2. 9
0, 1, 23, 66, 130, 215, 321, 448, 596, 765, 955, 1166, 1398, 1651, 1925, 2220, 2536, 2873, 3231, 3610, 4010, 4431, 4873, 5336, 5820, 6325, 6851, 7398, 7966, 8555, 9165, 9796, 10448, 11121, 11815, 12530, 13266, 14023, 14801, 15600 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 23, ..., and the parallel line from 1, in the direction 1, 66, ..., in the square spiral whose vertices are the generalized 23-gonal numbers. - Omar E. Pol, Jul 18 2012
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
LINKS
FORMULA
G.f.: x*(1+20*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 21*n + a(n-1) - 20 with n > 0, a(0) = 0. - Vincenzo Librandi, Aug 06 2010
a(n) = A226491(n) - n. - Bruno Berselli, Jun 11 2013
a(21*a(n)+211*n+1) = a(21*a(n)+211*n) + a(21*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 21/23. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 21*x^2/2). - Nikolaos Pantelidis, Feb 06 2023
MATHEMATICA
CoefficientList[Series[x (1 + 20 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
Table[(21n^2 - 19n)/2, {n, 0, 39}] (* Alonso del Arte, Jan 23 2015 *)
PolygonalNumber[23, Range[0, 40]] (* Harvey P. Dale, Aug 01 2022 *)
PROG
(PARI) a(n)=n*(21*n-19)/2 \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
Sequence in context: A316578 A323220 A001346 * A125872 A228611 A104945
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved

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Last modified April 16 22:07 EDT 2024. Contains 371755 sequences. (Running on oeis4.)