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A051867 15-gonal (or pentadecagonal) numbers: n(13n-11)/2. 15
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
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
E.g.f.: exp(x)*(x + 13*x^2/2). - Nikolaos Pantelidis, Feb 06 2023
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)