A037140 Convolution of natural numbers n >= 1 with Fibonacci numbers F(k), for k >= 5.

5, 18, 44, 91, 172, 308, 533, 902, 1504, 2483, 4072, 6648, 10821, 17578, 28516, 46219, 74868, 121228, 196245, 317630, 514040, 831843, 1346064, 2178096, 3524357, 5702658, 9227228, 14930107, 24157564, 39087908, 63245717, 102333878, 165579856, 267914003

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, A033937, A033960.

Programs

GAP

List([0..40], n-> Fibonacci(n+9) -8*n-29) # G. C. Greubel, Jul 05 2019

Magma

[Fibonacci(n+9) -8*n-29: n in [0..40]]; // G. C. Greubel, Jul 05 2019

Mathematica

Table[Fibonacci[n+9] -8*n-29, {n,0,40}] (* G. C. Greubel, Jul 05 2019 *)

PARI

vector(40, n, n--; fibonacci(n+9) -8*n-29) \\ G. C. Greubel, Jul 05 2019

Sage

[fibonacci(n+9) -8*n-29 for n in (0..40)] # G. C. Greubel, Jul 05 2019

Formula

a(n) = Fibonacci(n+9) - (29+8*n).

G.f.: (5+3*x)/((1-x-x^2)*(1-x)^2).

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006