OFFSET
0,3
COMMENTS
The g.f. for compositions of k_1 kinds of 1's, k_2 kinds of 2's, ..., k_j kinds of j's, ... is 1/(1-sum(j>=1, k_j * x^j )).
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,3,-1).
FORMULA
a(n) = +2*a(n-1) +3*a(n-2) -1*a(n-3).
G.f.: ((1-x)^2*(1+x))/(1-2*x-3*x^2+x^3).
G.f.: 1/(1-sum(j>=1, floor((3*j)/2)*x^j )).
MATHEMATICA
LinearRecurrence[{2, 3, -1}, {1, 1, 4, 11}, 50] (* Paolo Xausa, Nov 14 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jul 06 2011
STATUS
approved