OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
G.f.: (x^4 + 2*x^3 + 4*x^2 + 2*x + 1) / ((1 - x)^2*(1 - x^3)).
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. - Colin Barker, Jan 27 2018
From Stefano Spezia, Apr 06 2023: (Start)
a(n) = (8 + 15*n + 15*n^2 + A061347(n+2))/9.
E.g.f.: exp(-x/2)*(exp(3*x/2)*(8 + 30*x + 15*x^2) + cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/9. (End)
MATHEMATICA
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 4, 11, 21, 34}, 50] (* Paolo Xausa, Feb 24 2026 *)
PROG
(PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Jan 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 26 2018
STATUS
approved