

A051875


23gonal numbers: a(n) = n(21n19)/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
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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 23gonal 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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x*(1+20*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(n) = 21*n + a(n1)  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


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*n19)/2 \\ Charles R Greathouse IV, Jan 24 2014


CROSSREFS

Sequence in context: A316578 A323220 A001346 * A125872 A228611 A104945
Adjacent sequences: A051872 A051873 A051874 * A051876 A051877 A051878


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



