

A051871


19gonal (or enneadecagonal) numbers: n(17n15)/2.


5



0, 1, 19, 54, 106, 175, 261, 364, 484, 621, 775, 946, 1134, 1339, 1561, 1800, 2056, 2329, 2619, 2926, 3250, 3591, 3949, 4324, 4716, 5125, 5551, 5994, 6454, 6931, 7425, 7936, 8464, 9009, 9571, 10150, 10746, 11359, 11989, 12636, 13300
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 19,... and the parallel line from 1, in the direction 1, 54,..., in the square spiral whose vertices are the generalized 19gonal numbers.  Omar E. Pol, Jul 18 2012.
Partial sums of A215137 = 17n + 1. Jeremy Gardiner, Aug 04 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

Jeremy Gardiner, Table of n, a(n) for n = 0..999
Index to sequences with linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = n(17n15)/2.
G.f.: x*(1+16*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(n) = 17*n+a(n1)16 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
a(17*a(n)+137*n+1) = a(17*a(n)+137*n) + a(17*n+1).  Vladimir Shevelev, Jan 24 2014


EXAMPLE

a(1)=17*1+016=1; a(2)=17*2+116=19; a(3)=17*3+1916=54 [From Vincenzo Librandi, Aug 06 2010]


MAPLE

A051871 := proc(n) n*(17*n15)/2 ; end proc: seq(A051871(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!, 17}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]


PROG

(PARI) n*(17*n15)/2 \\ Charles R Greathouse IV, Jan 24 2014


CROSSREFS

Cf. ngonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865A051870, this sequence, A051872A051876.
Sequence in context: A242797 A142072 A221594 * A044121 A044502 A069131
Adjacent sequences: A051868 A051869 A051870 * A051872 A051873 A051874


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



