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A051872 20-gonal (or icosagonal) numbers: n(9n-8). 7
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 (list; graph; refs; listen; history; text; internal format)
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 20-gonal 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

Ivan Panchenko, 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) = 18*n+a(n-1)-17, with n>0, a(0)=0. [Vincenzo Librandi, Aug 06 2010]

G.f.: x*(1+17*x)/(1-x)^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*n-8) ; end proc: seq(A051872(n), n=0..30) ; # R. J. Mathar, Feb 05 2011

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 18}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

PROG

(PARI) n*(9*n-8) \\ Charles R Greathouse IV, Jan 24 2014

CROSSREFS

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051871, this sequence, A051873-A051876.

Sequence in context: A109806 A216267 A012483 * A104100 A069132 A124713

Adjacent sequences:  A051869 A051870 A051871 * A051873 A051874 A051875

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified October 20 14:23 EDT 2014. Contains 248338 sequences.