|
| |
|
|
A051867
|
|
15-gonal (or pentadecagonal) numbers: n(13n-11)/2.
|
|
10
|
|
|
|
0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242, 2490, 2751, 3025, 3312, 3612, 3925, 4251, 4590, 4942, 5307, 5685, 6076, 6480, 6897, 7327, 7770, 8226, 8695, 9177, 9672, 10180, 10701
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Sequence found by reading the line from 0, in the direction 0, 15,... and the parallel line from 1, in the direction 1, 42,..., in the square spiral whose vertices are the generalized 15-gonal numbers. - Omar E. Pol, Jul 18 2012
|
|
|
REFERENCES
|
Albert 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
|
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
G.f.: x*(1+12*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 13*n+a(n-1)-12 (with a(0)=0) - Vincenzo Librandi, Aug 06 2010
a(0)=0, a(1)=1, a(2)=15, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Feb 29 2012
a(13*a(n)+79*n+1) = a(13*a(n)+79*n) + a(13*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 13/15. - Amiram Eldar, Jan 21 2021
|
|
|
MATHEMATICA
|
Table[n (13n-11)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 15}, 50] (* Harvey P. Dale, Feb 29 2012 *)
|
|
|
PROG
|
(PARI) a(n)=n*(13*n-11)/2 \\ Charles R Greathouse IV, Oct 07 2015
|
|
|
CROSSREFS
|
Sequence in context: A325041 A154267 A173351 * A008976 A280232 A233302
Adjacent sequences: A051864 A051865 A051866 * A051868 A051869 A051870
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Dec 15 1999
|
|
|
STATUS
|
approved
|
| |
|
|
