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A051876 24-gonal numbers: a(n) = n*(11*n-10). 11
0, 1, 24, 69, 136, 225, 336, 469, 624, 801, 1000, 1221, 1464, 1729, 2016, 2325, 2656, 3009, 3384, 3781, 4200, 4641, 5104, 5589, 6096, 6625, 7176, 7749, 8344, 8961, 9600, 10261, 10944, 11649, 12376, 13125, 13896, 14689, 15504, 16341 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 24,... and the parallel line from 1, in the direction 1, 69,..., in the square spiral whose vertices are the generalized 24-gonal numbers. - Omar E. Pol, Jul 18 2012
This is also a star dodecagonal number: a(n) = A051624(n) + 12*A000217(n-1). - Luciano Ancora, Mar 30 2015
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
a(n) = 22*n+a(n-1)-21, with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010
G.f.: x*(1+21*x)/(1-x)^3. - Colin Barker, Jan 10 2012
a(22*a(n)+232*n+1) = a(22*a(n)+232*n) + a(22*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 11/12. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 11*x^2). - Nikolaos Pantelidis, Feb 05 2023
MAPLE
A051876:=n->n*(11*n - 10); seq(A051876(n), n=0..50); # Wesley Ivan Hurt, Feb 25 2014
MATHEMATICA
Table[n (11 n - 10), {n, 0, 50}] (* Wesley Ivan Hurt, Feb 25 2014 *)
PROG
(PARI) a(n)=n*(11*n-10) \\ Charles R Greathouse IV, Jul 19 2011
CROSSREFS
Sequence in context: A087406 A319972 A304157 * A069174 A124717 A126378
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved

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Last modified March 3 21:06 EST 2024. Contains 370517 sequences. (Running on oeis4.)