A067334 Convolution of Fibonacci F(n+1), n>=0, with F(n+6), n>=0.

8, 21, 50, 105, 210, 404, 758, 1395, 2530, 4535, 8052, 14184, 24820, 43185, 74770, 128901, 221382, 378940, 646690, 1100655, 1868738, 3165811, 5352360, 9032400, 15216800, 25595469, 42990578, 72110625, 120804090, 202142180, 337876622, 564176619, 941141410

Offset: 0

Author

Wolfdieter Lang, Feb 15 2002

Keywords

• nonn
• easy
• changed

Comments

Sixth diagonal of A067330. Sixth column of A067418.

Links

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

Crossrefs

Cf. A067330, A067418.

Programs

Mathematica

CoefficientList[Series[(8+5x)/(1-x-x^2)^2,{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-2,-1},{8,21,50,105},40] (* Harvey P. Dale, Apr 07 2012 *)

Formula

a(n) = A067330(n+5, n) = A067418(n+5, 5) = Sum_{k=0..n} F(k+1)*F(n+6-k), n>=0.

a(n) = ((29*n+40)*F(n+1)+18*(n+1)*F(n))/5, with F(n) := A000045(n) (Fibonacci).

G.f.: (8+5*x)/(1-x-x^2)^2.

a(0)=8, a(1)=21, a(2)=50, a(3)=105, a(n) = 2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). - Harvey P. Dale, Apr 07 2012

Extensions

More terms from Jason Yuen, Aug 27 2025