OFFSET
0,2
COMMENTS
a(n) is the number of generalized compositions of n when there are 2*i+1 different types of i, (i=1,2,...). - Milan Janjic, Sep 24 2010
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Daniel Birmajer, Juan B. Gil, and Michael D. Weiner, (an + b)-color compositions, arXiv:1707.07798 [math.CO], 2017.
Stéphane Ouvry and Alexios P. Polychronakos, Signed area enumeration for lattice walks, Séminaire Lotharingien de Combinatoire (2023) Vol. 87B.
N. J. A. Sloane, Transforms
Index entries for linear recurrences with constant coefficients, signature (5,-2).
FORMULA
G.f.: (x^2-2*x+1)/(2*x^2-5*x+1).
G.f.: 1 / (1 - 3*x - 5*x^2 - 7*x^3 - 9*x^4 - 11*x^5 - ...). - Gary W. Adamson, Jul 27 2009
a(n) = 5*a(n-1) - 2*a(n-2) with a(1) = 3, a(2) = 14, for n >= 3. - Taras Goy, Mar 19 2019
a(n) = (2^(-2-n)*((5-sqrt(17))^n*(-7+sqrt(17)) + (5+sqrt(17))^n*(7+sqrt(17)))) / sqrt(17) for n > 0. - Colin Barker, Mar 19 2019
MATHEMATICA
Join[{1}, LinearRecurrence[{5, -2}, {3, 14}, 22]] (* Jean-François Alcover, Aug 07 2018 *)
PROG
(PARI) Vec((1 - x)^2 / (1 - 5*x + 2*x^2) + O(x^25)) \\ Colin Barker, Mar 19 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Apr 27 2001
STATUS
approved