OFFSET
0,3
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 17,... and the parallel line from 1, in the direction 1, 48,..., in the square spiral whose vertices are the generalized 17-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
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(1+14*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = a(n-1) + 15*n - 14 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010
a(n) = A226489(n) - n. - Bruno Berselli, Jun 11 2013
a(15*a(n) + 106*n + 1) = a(15*a(n) + 106*n) + a(15*n+1). - Vladimir Shevelev, Jan 24 2014
E.g.f.: x*(2 + 15*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019
Product_{n>=2} (1 - 1/a(n)) = 15/17. - Amiram Eldar, Jan 22 2021
MAPLE
MATHEMATICA
Table[n*(15*n - 13)/2, {n, 0, 40}] (* Robert Price, Oct 11 2018 *)
PolygonalNumber[17, Range[0, 50]] (* Harvey P. Dale, Dec 14 2022 *)
PROG
(PARI) a(n)=n*(15*n-13)/2 \\ Charles R Greathouse IV, Jan 24 2014
(Magma) [n*(15*n-13)/2: n in [0..40]]; // G. C. Greubel, Aug 30 2019
(Sage) [n*(15*n-13)/2 for n in (0..40)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n-> n*(15*n-13)/2); # G. C. Greubel, Aug 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved