A037141 Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), for k >= -5, with F(-n)=(-1)^(n+1)*F(n);.

5, 7, 11, 14, 18, 22, 27, 33, 41, 52, 68, 92, 129, 187, 279, 426, 662, 1042, 1655, 2645, 4245, 6832, 11016, 17784, 28733, 46447, 75107, 121478, 196506, 317902, 514323, 832137, 1346369, 2178412, 3524684, 5702996, 9227577, 14930467, 24157935, 39088290

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Crossrefs

Cf. A000045, A000071, A002062.

Programs

Mathematica

CoefficientList[Series[(5-8x)/((1-x-x^2)(1-x)^2),{x,0,40}],x] (* or *) LinearRecurrence[{3,-2,-1,1},{5,7,11,14},40] (* Harvey P. Dale, Nov 06 2017 *)

Formula

a(n) = F(n-1)+(4+3*n); G.f.: (5-8*x)/((1-x-x^2)*(1-x)^2)

Extensions

More terms from Harvey P. Dale, Nov 06 2017