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A051876 24-gonal numbers: n*(11*n-10). 30
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

REFERENCES

A. 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 with 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

MAPLE

A051876:=n->n*(11*n - 10); seq(A051876(n), n=0..50); # Wesley Ivan Hurt, Feb 25 2014

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 22}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

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

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051875.

Sequence in context: A039331 A043934 A087406 * A069174 A124717 A126378

Adjacent sequences:  A051873 A051874 A051875 * A051877 A051878 A051879

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified April 24 00:39 EDT 2014. Contains 240947 sequences.