A332001 Number of compositions (ordered partitions) of n into distinct parts that do not divide n.

1, 0, 0, 0, 0, 2, 0, 4, 2, 4, 4, 20, 2, 34, 14, 20, 14, 146, 8, 244, 22, 140, 202, 956, 16, 782, 596, 752, 216, 5786, 82, 10108, 640, 4016, 5200, 6028, 218, 53674, 14570, 19004, 980, 152810, 1786, 245884, 13588, 16534, 108382, 719156, 1494, 532532, 54316

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to compositions

Example

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

Maple

a:= proc(n) local b, l; l, b:= numtheory[divisors](n),
      proc(m, i, p) option remember; `if`(m=0, p!, `if`(i<2, 0,
        b(m, i-1, p)+`if`(i>m or i in l, 0, b(m-i, i-1, p+1))))
      end; forget(b): b(n, n-1, 0)
    end:
seq(a(n), n=0..63);  # Alois P. Heinz, Feb 04 2020

Mathematica

a[n_] := Module[{b, l = Divisors[n]}, b[m_, i_, p_] := b[m, i, p] = If[m == 0, p!, If[i < 2, 0, b[m, i - 1, p] + If[i > m || MemberQ[l, i], 0, b[m - i, i - 1, p + 1]]]]; b[n, n - 1, 0]];
a /@ Range[0, 63] (* Jean-François Alcover, Nov 30 2020, after Alois P. Heinz *)

Crossrefs

Cf. A018818, A032020, A033630, A098743, A100346, A200745, A300702, A331927, A331979.

Sequence in context: A079534 A229910 A097042 * A196606 A371130 A361391

Adjacent sequences: A331998 A331999 A332000 * A332002 A332003 A332004

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2020

Status

approved