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A051866
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14-gonal (or tetradecagonal) numbers: n*(6*n-5).
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17
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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
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0,3
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COMMENTS
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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
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
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LINKS
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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).
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FORMULA
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a(n) = n*(6*n-5).
G.f.: x*(1+11*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 12*n+a(n-1)-11 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
a(n) = A033568(n) - 1. - Omar E. Pol, Jul 18 2012
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EXAMPLE
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a(1)=12*1+0-11=1; a(2)=12*2+1-11=14; a(3)=12*3+14-11=39 [From Vincenzo Librandi, Aug 06 2010]
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MAPLE
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A051866 := proc(n) n*(6*n-5) ; end proc: seq(A051866(n), n=0..30) ; # R. J. Mathar, Feb 05 2011
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 12}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 15 2008]
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, this sequence, A051867-A051876.
Sequence in context: A044091 A044472 A178564 * A162266 A181149 A019063
Adjacent sequences: A051863 A051864 A051865 * A051867 A051868 A051869
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Dec 15 1999
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STATUS
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approved
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