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

Author

N. J. A. Sloane, Dec 15 1999

Keywords

• nonn
• easy

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).

Programs

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 *)

PARI

a(n)=n*(11*n-10) \\ Charles R Greathouse IV, Jul 19 2011

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