A332309 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 3.

1, 1, 1, 2, 1, 3, 4, 9, 9, 6, 15, 17, 38, 29, 53, 70, 65, 91, 150, 229, 277, 236, 439, 489, 514, 897, 993, 1632, 1521, 2339, 2972, 3257, 4121, 5992, 5303, 7729, 10932, 15157, 17653, 18398, 26305, 31683, 34408, 51885, 58173, 61098, 90519, 101249, 143402, 156905

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(9) = 6 because we have [8, 1], [7, 2], [5, 4], [4, 5], [2, 7] and [1, 8].

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, 3), 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, 3], 1, n/i]}]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 55] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000726, A003105, A032020, A032021, A332310, A332311.

Sequence in context: A134876 A019612 A007444 * A166476 A052950 A086851

Adjacent sequences: A332306 A332307 A332308 * A332310 A332311 A332312

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 09 2020

Status

approved