OFFSET
0,3
COMMENTS
This sequence does not contain any squares other than 0 and 1. See A188896. - T. D. Noe, Apr 13 2011
Sequence found by reading the line from 0, in the direction 0, 20,... and the parallel line from 1, in the direction 1, 57,..., in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 18 2012
This is also a star decagonal number: a(n) = A001107(n) + 10*A000217(n-1). - Luciano Ancora, Mar 30 2015
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
a(n) = 18*n + a(n-1) - 17, with n > 0, a(0) = 0. - Vincenzo Librandi, Aug 06 2010
G.f.: x*(1+17*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(18*a(n) + 154*n + 1) = a(18*a(n) + 154*n) + a(18*n + 1). - Vladimir Shevelev, Jan 24 2014
Product_{n>=2} (1 - 1/a(n)) = 9/10. - Amiram Eldar, Jan 22 2021
For n>0, a(n) = A002378(3*n-2) + n - 2. - Charlie Marion, Jul 18 2022
E.g.f.: exp(x)*(x + 9*x^2). - Nikolaos Pantelidis, Feb 05 2023
MAPLE
MATHEMATICA
Table[9n^2 - 8n, {n, 0, 59}] (* Alonso del Arte, Dec 20 2014 *)
PolygonalNumber[20, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 14 2017 *)
PROG
(PARI) n*(9*n-8) \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved