A213044 Convolution of Fibonacci numbers and positive integers repeated three times (A000045 and A008620).

1, 1, 2, 5, 7, 12, 22, 34, 56, 94, 150, 244, 399, 643, 1042, 1691, 2733, 4424, 7164, 11588, 18752, 30348, 49100, 79448, 128557, 208005, 336562, 544577, 881139, 1425716, 2306866, 3732582, 6039448, 9772042, 15811490, 25583532, 41395035

Offset: 0

Author

Clark Kimberling, Jun 10 2012

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 1, 2, -2, -2, -1, 1, 1).

Crossrefs

Cf. A213500.

Programs

Mathematica

f[x_] := (1 - x^3)^2; g[x] := 1 - x - x^2;
s = Normal[Series[1/(f[x] g[x]), {x, 0, 60}]]
c = CoefficientList[s, x]  (* A213044 *)

Formula

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-2*a(n-4)-a(n-5)+a(n-6)+a(n-7).

G.f.: 1/((1 - x - x^2)*(1 - x^3)^2).