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
Partial sums of A215144. - Leo Tavares, Mar 17 2023
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
Vincenzo Librandi, 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+18*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 19*n+a(n-1)-18 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010
a(n) = A226490(n) - n. - Bruno Berselli, Jun 11 2013
a(19*a(n)+172*n+1) = a(19*a(n)+172*n) + a(19*n+1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 19/21. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 19*x^2/2). - Nikolaos Pantelidis, Feb 06 2023
MAPLE
MATHEMATICA
PolygonalNumber[21, Range[0, 40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 22 2016 *)
Table[n*(19*n - 17)/2, {n, 0, 100}] (* Robert Price, Oct 11 2018 *)
PROG
(PARI) n*(19*n-17)/2 \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved