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

0,3

Links

Table of n, a(n) for n=0..36.

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

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).

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 *)

Crossrefs

Cf. A213500.

Sequence in context: A359064 A333068 A029938 * A269769 A230428 A071013

Adjacent sequences: A213041 A213042 A213043 * A213045 A213046 A213047

Keyword

nonn,easy

Author

Clark Kimberling, Jun 10 2012

Status

approved