A357690 Number of ways to write n as an ordered sum of five positive Fibonacci numbers (with a single type of 1).

1, 5, 15, 30, 50, 71, 95, 115, 140, 165, 191, 205, 220, 240, 260, 285, 310, 325, 325, 320, 341, 350, 380, 385, 405, 420, 430, 450, 465, 465, 445, 410, 435, 425, 450, 481, 495, 515, 490, 510, 555, 525, 580, 540, 530, 570, 530, 580, 600, 520, 525, 440, 455, 520, 445, 555, 530

Offset: 5

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..10000

Crossrefs

Cf. A000045, A076739, A121548, A121549, A121550, A319398, A357688, A357691.

Programs

Mathematica

nmax = 61; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^5.

a(n) = A121548(n,5).