A332311 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 5.

1, 1, 1, 3, 3, 4, 9, 11, 11, 19, 44, 31, 61, 87, 117, 144, 279, 311, 389, 541, 640, 1003, 1225, 2145, 2493, 3452, 3507, 5417, 6671, 8821, 11580, 17959, 21043, 26289, 34797, 41536, 59637, 72707, 85871, 110947, 172472, 175873, 249691, 327801, 418779, 512748

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Example

a(6) = 9 because we have [6], [4, 2], [3, 2, 1], [3, 1, 2], [2, 4], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].

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, 5), 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, 5], 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. A032020, A032021, A035959, A096938, A332309, A332310.

Sequence in context: A185395 A060372 A128036 * A332340 A045794 A065678

Adjacent sequences: A332308 A332309 A332310 * A332312 A332313 A332314

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 09 2020

Status

approved