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A359516 Number of compositions (ordered partitions) of n into at most 4 positive Fibonacci numbers (with a single type of 1).

%I A359516 #13 Feb 13 2023 07:45:37
%S A359516 1,1,2,4,7,13,20,27,35,40,46,50,55,60,61,60,65,68,72,76,73,72,66,66,
%T A359516 79,73,85,80,79,90,76,84,85,60,72,56,69,85,69,99,89,70,97,73,94,97,66,
%U A359516 90,72,70,96,60,85,60,24,72,44,71,88,57,105,85,78,111,74,97,82,48,97,69,79
%N A359516 Number of compositions (ordered partitions) of n into at most 4 positive Fibonacci numbers (with a single type of 1).
%F A359516 a(n) = Sum_{k=0..4} A121548(n,k). - _Alois P. Heinz_, Jan 03 2023
%p A359516 g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
%p A359516 b:= proc(n, t) option remember; `if`(n=0, 1, `if`(t<1, 0,
%p A359516       add(`if`(g(j), b(n-j, t-1), 0), j=1..n)))
%p A359516     end:
%p A359516 a:= n-> b(n, 4):
%p A359516 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jan 03 2023
%t A359516 g[n_] := Function[t, IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 4]][5 n^2];
%t A359516 b[n_, t_] := b[n, t] = If[n == 0, 1, If[t < 1, 0, Sum[If[g[j], b[n - j, t - 1], 0], {j, 1, n}]]];
%t A359516 a[n_] := b[n, 4];
%t A359516 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Feb 13 2023, after _Alois P. Heinz_ *)
%Y A359516 Cf. A000045, A076739, A121548, A357688, A359513, A359514, A359515.
%K A359516 nonn
%O A359516 0,3
%A A359516 _Ilya Gutkovskiy_, Jan 03 2023