A033937 Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), k >= 3.

2, 7, 17, 35, 66, 118, 204, 345, 575, 949, 1556, 2540, 4134, 6715, 10893, 17655, 28598, 46306, 74960, 121325, 196347, 317737, 514152, 831960, 1346186, 2178223, 3524489, 5702795, 9227370, 14930254, 24157716

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Crossrefs

Cf. A000045, A001924, A001891.

Programs

GAP

List([0..40], n-> Fibonacci(n+7) -3*n-11) # G. C. Greubel, Jul 05 2019

Magma

[Fibonacci(n+7) -3*n-11: n in [0..40]]; // G. C. Greubel, Jul 05 2019

Mathematica

Table[Fibonacci[n+7] -3*n-11, {n,0,40}] (* G. C. Greubel, Jul 05 2019 *)

PARI

vector(40, n, n--; fibonacci(n+7) -3*n-11) \\ G. C. Greubel, Jul 05 2019

Sage

[fibonacci(n+7) -3*n-11 for n in (0..40)] # G. C. Greubel, Jul 05 2019

Formula

a(n) = Fibonacci(n+7) - (11+3*n).

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