A051876 24-gonal numbers: a(n) = n*(11*n-10).

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

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

Ivan Panchenko, 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

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

Adjacent sequences: A051873 A051874 A051875 * A051877 A051878 A051879

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 1999

Status

approved