

A051872


20gonal (or icosagonal) numbers: a(n) = n*(9*n8).


11



0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097, 3440, 3801, 4180, 4577, 4992, 5425, 5876, 6345, 6832, 7337, 7860, 8401, 8960, 9537, 10132, 10745, 11376, 12025, 12692, 13377, 14080
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OFFSET

0,3


COMMENTS

This sequence does not contain any squares other than 0 and 1. See A188896.  T. D. Noe, Apr 13 2011
Sequence found by reading the line from 0, in the direction 0, 20,... and the parallel line from 1, in the direction 1, 57,..., in the square spiral whose vertices are the generalized 20gonal numbers.  Omar E. Pol, Jul 18 2012
This is also a star decagonal number: a(n) = A001107(n) + 10*A000217(n1).  Luciano Ancora, Mar 30 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

Ivan Panchenko, 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

a(n) = 18*n + a(n1)  17, with n > 0, a(0) = 0.  Vincenzo Librandi, Aug 06 2010
G.f.: x*(1+17*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(18*a(n) + 154*n + 1) = a(18*a(n) + 154*n) + a(18*n + 1).  Vladimir Shevelev, Jan 24 2014


MAPLE

A051872 := proc(n) n*(9*n8) ; end proc: seq(A051872(n), n=0..30) ; # R. J. Mathar, Feb 05 2011


MATHEMATICA

Table[9n^2  8n, {n, 0, 59}] (* Alonso del Arte, Dec 20 2014 *)
PolygonalNumber[20, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 14 2017 *)


PROG

(PARI) n*(9*n8) \\ Charles R Greathouse IV, Jan 24 2014


CROSSREFS

Sequence in context: A109806 A216267 A012483 * A297397 A104100 A069132
Adjacent sequences: A051869 A051870 A051871 * A051873 A051874 A051875


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



