cp's OEIS Frontend

A359515 Number of compositions (ordered partitions) of n into at most 3 positive Fibonacci numbers (with a single type of 1).

%I A359515 #11 May 28 2023 04:04:55
%S A359515 1,1,2,4,6,9,10,11,12,12,12,14,12,12,11,12,15,12,14,12,6,12,8,14,15,9,
%T A359515 15,12,9,14,6,12,6,0,12,8,11,17,9,15,9,6,15,9,12,9,0,14,6,6,12,0,6,0,
%U A359515 0,12,8,11,14,9,17,9,6,15,6,9,6,0,15,9,9,12,0,9,0,0,14,6,6,6,0,12
%N A359515 Number of compositions (ordered partitions) of n into at most 3 positive Fibonacci numbers (with a single type of 1).
%F A359515 a(n) = Sum_{k=0..3} A121548(n,k). - _Alois P. Heinz_, Jan 03 2023
%p A359515 g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
%p A359515 b:= proc(n, t) option remember; `if`(n=0, 1, `if`(t<1, 0,
%p A359515       add(`if`(g(j), b(n-j, t-1), 0), j=1..n)))
%p A359515     end:
%p A359515 a:= n-> b(n, 3):
%p A359515 seq(a(n), n=0..81);  # _Alois P. Heinz_, Jan 03 2023
%t A359515 g[n_] := With[{t = 5 n^2}, IntegerQ @ Sqrt[t+4] || IntegerQ @ Sqrt[t-4]];
%t A359515 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 A359515 a[n_] :=  b[n, 3];
%t A359515 Table[a[n], {n, 0, 81}] (* _Jean-François Alcover_, May 28 2023, after _Alois P. Heinz_ *)
%Y A359515 Cf. A000045, A076739, A121548, A121550, A359512, A359514, A359516.
%K A359515 nonn
%O A359515 0,3
%A A359515 _Ilya Gutkovskiy_, Jan 03 2023