login
Number of ways to write n as an ordered sum of ten positive Fibonacci numbers (with a single type of 1).
0

%I #6 Oct 11 2022 06:00:13

%S 1,10,55,210,625,1542,3300,6310,11040,17980,27673,40660,57475,78520,

%T 104175,134742,170620,212220,260035,314290,374933,441790,514855,

%U 594210,680070,772582,871920,977790,1090680,1210960,1339417,1475340,1618020,1766080,1918785,2076012

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

%F G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^10.

%F a(n) = A121548(n,10).

%t nmax = 45; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

%Y Cf. A000045, A076739, A121548, A121549, A121550, A319403, A357688, A357690, A357691, A357694, A357716, A357717.

%K nonn

%O 10,2

%A _Ilya Gutkovskiy_, Oct 11 2022