A332310 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 4.

1, 1, 1, 3, 2, 3, 9, 5, 12, 17, 23, 43, 50, 55, 67, 111, 144, 273, 291, 377, 410, 689, 827, 961, 1860, 1663, 2647, 3573, 4610, 4683, 6753, 8465, 11232, 16835, 19985, 24073, 29258, 40411, 51367, 58431, 72084, 99807, 119409, 176387, 199922, 250841, 290123

Offset

0,4

Links

Table of n, a(n) for n=0..46.

Index entries for sequences related to compositions

Example

a(7) = 5 because we have [7], [6, 1], [5, 2], [2, 5] and [1, 6].

Maple

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
      p!, add(b(n-i*j, i-1, p+j), j=0..min(irem(i, 4), 1, n/i))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..55);  # Alois P. Heinz, Feb 09 2020

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!, Sum[b[n - i j, i - 1, p + j], {j, 0, Min[Mod[i, 4], 1, n/i]}]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 55] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *)

Crossrefs

Cf. A001935, A032020, A032021, A070048, A332309, A332311.

Sequence in context: A360701 A216829 A331846 * A022460 A010605 A120879

Adjacent sequences: A332307 A332308 A332309 * A332311 A332312 A332313

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 09 2020

Status

approved