A067977 Convolution of Fibonacci F(n+1), n>=0, with F(n+9), n>=0.

34, 89, 212, 445, 890, 1712, 3212, 5911, 10720, 19215, 34116, 60096, 105158, 182965, 316780, 546113, 937918, 1605424, 2739760, 4662995, 7916984, 13412019, 22675272, 38265600, 64465450, 108433937

Offset: 0

Author

Wolfdieter Lang, Feb 15 2002

Keywords

• nonn
• easy

Comments

Ninth diagonal of A067330. Ninth column of A067418.

Links

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

Crossrefs

Cf. A000045, A000204, A067330, A067418.

Programs

Mathematica

CoefficientList[Series[(34 + 21*x)/(1 - x - x^2)^2, {x, 0, 30}], x] (* Wesley Ivan Hurt, Feb 16 2017 *)
LinearRecurrence[{2,1,-2,-1},{34,89,212,445},30] (* Harvey P. Dale, Dec 22 2022 *)

Formula

a(n) = A067330(n+8, n) = A067418(n+8, 8) = Sum_{k=0..n} F(k+1)*F(n+9-k), n>=0.

G.f.: (34+21*x)/(1-x-x^2)^2.

a(n) = ((123*n+5*34)*F(n+1)+76*(n+1)*F(n))/5, F(n) := A000045(n) (Fibonacci); 34=F(9), 76=L(9), 123=L(10), L(n) := A000204(n) (Lucas).