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A051873 21-gonal numbers: n(19n-17)/2. 5
0, 1, 21, 60, 118, 195, 291, 406, 540, 693, 865, 1056, 1266, 1495, 1743, 2010, 2296, 2601, 2925, 3268, 3630, 4011, 4411, 4830, 5268, 5725, 6201, 6696, 7210, 7743, 8295, 8866, 9456, 10065, 10693, 11340, 12006, 12691, 13395, 14118 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 21,... and the parallel line from 1, in the direction 1, 60,..., in the square spiral whose vertices are the generalized 21-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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(1+18*x)/(1-x)^3. [Bruno Berselli, Feb 04 2011]

a(n) = 19*n+a(n-1)-18 with n>0, a(0)=0. [ Vincenzo Librandi, Aug 06 2010]

a(n) = A226490(n) - n. [Bruno Berselli, Jun 11 2013]

a(19*a(n)+172*n+1) = a(19*a(n)+172*n) + a(19*n+1). - Vladimir Shevelev, Jan 24 2014

MAPLE

A051873 := proc(n) n*(19*n-17)/2 ; end proc: seq(A051873(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!, 19}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

PROG

(PARI) n*(19*n-17)/2 \\ Charles R Greathouse IV, Jan 24 2014

CROSSREFS

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051872, this sequence, A051874-A051876.

Sequence in context: A020148 A037305 A223467 * A223460 A219690 A069133

Adjacent sequences:  A051870 A051871 A051872 * A051874 A051875 A051876

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified April 20 22:29 EDT 2014. Contains 240823 sequences.