A359515 - OEIS

%I #11 May 28 2023 04:04:55

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

%F a(n) = Sum_{k=0..3} A121548(n,k). - _Alois P. Heinz_, Jan 03 2023

%p g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:

%p b:= proc(n, t) option remember; `if`(n=0, 1, `if`(t<1, 0,

%p       add(`if`(g(j), b(n-j, t-1), 0), j=1..n)))

%p     end:

%p a:= n-> b(n, 3):

%p seq(a(n), n=0..81);  # _Alois P. Heinz_, Jan 03 2023

%t g[n_] := With[{t = 5 n^2}, IntegerQ @ Sqrt[t+4] || IntegerQ @ Sqrt[t-4]];

%t 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 a[n_] :=  b[n, 3];

%t Table[a[n], {n, 0, 81}] (* _Jean-François Alcover_, May 28 2023, after _Alois P. Heinz_ *)

%Y Cf. A000045, A076739, A121548, A121550, A359512, A359514, A359516.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 03 2023