

A051866


14gonal (or tetradecagonal) numbers: n*(6*n5).


17



0, 1, 14, 39, 76, 125, 186, 259, 344, 441, 550, 671, 804, 949, 1106, 1275, 1456, 1649, 1854, 2071, 2300, 2541, 2794, 3059, 3336, 3625, 3926, 4239, 4564, 4901, 5250, 5611, 5984, 6369, 6766, 7175, 7596, 8029, 8474, 8931, 9400, 9881, 10374
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OFFSET

0,3


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 14,... and the parallel line from 1, in the direction 1, 39,..., in the square spiral whose vertices are the generalized 14gonal numbers A195818. Also sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 14,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318.  Omar E. Pol, Jul 18 2012
After 0, partial sums of A017533. [Bruno Berselli, Sep 11 2013]


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

T. D. Noe, 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) = n*(6*n5).
G.f.: x*(1+11*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(n) = 12*n+a(n1)11, with n>0, a(0)=0. [Vincenzo Librandi, Aug 06 2010]
a(n) = A033568(n)  1.  Omar E. Pol, Jul 18 2012
a(12*a(n)+67*n+1) = a(12*a(n)+67*n) + a(12*n+1).  Vladimir Shevelev, Jan 24 2014


MAPLE

A051866 := proc(n) n*(6*n5) ; end proc: seq(A051866(n), n=0..30) ; # R. J. Mathar, Feb 05 2011


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)


PROG

(PARI) a(n)=n*(6*n5); \\ Joerg Arndt, Feb 01 2014


CROSSREFS

Cf. ngonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, this sequence, A051867A051876.
Cf. A017533.
Sequence in context: A044091 A044472 A178564 * A162266 A181149 A019063
Adjacent sequences: A051863 A051864 A051865 * A051867 A051868 A051869


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



