

A051867


15gonal (or pentadecagonal) numbers: n(13n11)/2.


7



0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242, 2490, 2751, 3025, 3312, 3612, 3925, 4251, 4590, 4942, 5307, 5685, 6076, 6480, 6897, 7327, 7770, 8226, 8695, 9177, 9672, 10180, 10701
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OFFSET

0,3


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 15,... and the parallel line from 1, in the direction 1, 42,..., in the square spiral whose vertices are the generalized 15gonal 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

Harvey P. Dale, 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+12*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(n) = 13*n+a(n1)12 (with a(0)=0)  Vincenzo Librandi, Aug 06 2010
a(0)=0, a(1)=1, a(2)=15, a(n)=3*a(n1)3*a(n2)+a(n3).  Harvey P. Dale, Feb 29 2012
a(13*a(n)+79*n+1) = a(13*a(n)+79*n) + a(13*n+1).  Vladimir Shevelev, Jan 24 2014


MATHEMATICA

Table[n (13n11)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, 3, 1}, {0, 1, 15}, 50] (* Harvey P. Dale, Feb 29 2012 *)


PROG

(PARI) a(n)=n*(13*n11)/2 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Sequence in context: A070007 A154267 A173351 * A008976 A233302 A072119
Adjacent sequences: A051864 A051865 A051866 * A051868 A051869 A051870


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



