OFFSET
0,1
COMMENTS
If zero polygonal numbers are ignored, then for n >= 3, the a(n)-th n-gonal number is a sum of the (a(n)-1)-th n-gonal number and the (2*n-3)-th n-gonal number.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
W. Burrows, C. Tuffley, Maximising common fixtures in a round robin tournament with two divisions, arXiv preprint arXiv:1502.06664 [math.CO], 2015.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, Jan 21 2014: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -(18*x^2 - 23*x + 9)/(x-1)^3. (End)
E.g.f.: exp(x)*(9 - 5*x + 2*x^2). - Elmo R. Oliveira, Nov 13 2024
EXAMPLE
MATHEMATICA
Table[2 n^2 - 7 n + 9, {n, 0, 48}] (* Michael De Vlieger, Apr 19 2015 *)
LinearRecurrence[{3, -3, 1}, {9, 4, 3}, 50] (* Harvey P. Dale, Nov 24 2017 *)
PROG
(PARI) Vec(-(18*x^2-23*x+9)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jan 21 2014
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Vladimir Shevelev, Jan 21 2014
STATUS
approved