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 A051866 14-gonal (or tetradecagonal) numbers: a(n) = n*(6*n-5). 20
 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 (list; graph; refs; listen; history; text; internal format)
 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 14-gonal 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] This is also a star heptagonal number: a(n) = A000566(n) + 7*A000217(n-1). - Luciano Ancora, Mar 30 2015 Starting with offset 1, this is the binomial transform of (1, 13, 12, 0, 0, 0,...). - _Gary W. Adamson, Jul 29 2015 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 entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: x*(1+11*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(n) = 12*n+a(n-1)-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*n-5) ; 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*n-5); \\ Joerg Arndt, Feb 01 2014 CROSSREFS Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, this sequence, A051867-A051876. 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

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