A037157 Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), for k >= 6.

8, 29, 71, 147, 278, 498, 862, 1459, 2433, 4017, 6588, 10756, 17508, 28441, 46139, 74783, 121138, 196150, 317530, 513935, 831733, 1345949, 2177976, 3524232, 5702528, 9227093, 14929967, 24157419, 39087758, 63245562, 102333718

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, A037140.

Programs

GAP

List([0..40], n-> Fibonacci(n+10) -13*n-47); # G. C. Greubel, Jul 05 2019

Magma

[Fibonacci(n+10) -13*n-47: n in [0..40]]; // G. C. Greubel, Jul 05 2019

Mathematica

Table[Fibonacci[n+10] -13*n-47, {n,0,40}] (* G. C. Greubel, Jul 05 2019 *)
LinearRecurrence[{3,-2,-1,1},{8,29,71,147},40] (* Harvey P. Dale, Jun 30 2025 *)

PARI

vector(40, n, n--; fibonacci(n+10) -13*n-47) \\ G. C. Greubel, Jul 05 2019

Sage

[fibonacci(n+10) -13*n-47 for n in (0..40)] # G. C. Greubel, Jul 05 2019

Formula

a(n) = Fibonacci(n+10) - (47+13*n).

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