|
| |
|
|
A051871
|
|
19-gonal (or enneadecagonal) numbers: n(17n-15)/2.
|
|
10
|
|
|
|
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 19-gonal numbers. - Omar E. Pol, Jul 18 2012
Partial sums of A215137 (17n + 1). - Jeremy Gardiner, Aug 04 2012
|
|
|
REFERENCES
|
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
Elena Deza and Michel 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 related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
a(n) = n(17n-15)/2.
G.f.: x*(1+16*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 17*n + a(n-1) - 16 (with a(0) = 0). - 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
Product_{n>=2} (1 - 1/a(n)) = 17/19. - Amiram Eldar, Jan 22 2021
|
|
|
EXAMPLE
|
a(1) = 17 * 1 + 0 - 16 = 1.
a(2) = 17 * 2 + 1 - 16 = 19.
a(3) = 17 * 3 + 19 - 16 = 54. - Vincenzo Librandi, Aug 06 2010
|
|
|
MAPLE
|
A051871 := proc(n) n*(17*n-15)/2 ; end proc: seq(A051871(n), n=0..30) ; # R. J. Mathar, Feb 05 2011
|
|
|
MATHEMATICA
|
Table[(17n^2 - 15n)/2, {n, 0, 39}] (* Alonso del Arte, Feb 19 2015 *)
|
|
|
PROG
|
(PARI) a(n)=n*(17*n-15)/2; \\ Charles R Greathouse IV, Jan 24 2014
|
|
|
CROSSREFS
|
Sequence in context: A142072 A221594 A288144 * A044121 A044502 A069131
Adjacent sequences: A051868 A051869 A051870 * A051872 A051873 A051874
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Dec 15 1999
|
|
|
STATUS
|
approved
|
| |
|
|
