A161028 Number of partitions of n into Fibonacci numbers where every part appears at least 4 times.

1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 4, 2, 4, 4, 6, 5, 8, 7, 11, 9, 12, 11, 16, 16, 19, 19, 24, 24, 31, 29, 38, 37, 44, 47, 54, 57, 65, 68, 81, 80, 93, 95, 111, 116, 128, 136, 153, 158, 179, 184, 211, 216, 240, 253, 281, 294, 322, 337, 377, 388, 429, 445, 494, 515, 559, 587, 641, 669, 730

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n=1..1000 from R. H. Hardin)

Maple

F:= proc(n, i) option remember; (<<0|1>, <1|1>>^n)[1, 2] end:
b:= proc(n, i) option remember; `if`(n=0, 1, (f-> `if`(4*f<=n,
      add(b(n-j*f, i+1), j=[0, $4..n/f]), 0))(F(i)))
    end:
a:= n-> b(n, 2):
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 23 2019

Mathematica

F[n_] := F[n] = MatrixPower[{{0, 1}, {1, 1}}, n][[1, 2]];
b[n_, i_] := b[n, i] = If[n == 0, 1, Function[f, If[4*f <= n, Sum[b[n-j*f, i+1], {j, Join[{0}, Range[4, n/f]]}], 0]][F[i]]];
a[n_] := b[n, 2];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jan 28 2024, after Alois P. Heinz *)

Crossrefs

Cf. A000045.

Sequence in context: A297294 A161309 A161243 * A161079 A161295 A161270

Adjacent sequences: A161025 A161026 A161027 * A161029 A161030 A161031

Keyword

nonn

Author

R. H. Hardin, Jun 02 2009

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 23 2019

Status

approved