|
| |
|
|
A051873
|
|
21-gonal numbers: n(19n-17)/2.
|
|
4
|
|
|
|
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.
|
|
|
LINKS
|
Table of n, a(n) for n=0..39.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
a(n)=n(19n-17)/2.
G.f.: x*(1+18*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=19*n+a(n-1)-18 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
|
|
|
EXAMPLE
|
a(1)=19*1+0-18=1; a(2)=19*2+1-18=21; a(3)=19*3+21-18=60 [From Vincenzo Librandi, Aug 06 2010]
|
|
|
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 [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
|
|
|
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
|
|
|
AUTHOR
|
N. J. A. Sloane, Dec 15 1999
|
|
|
STATUS
|
approved
|
| |
|
|
