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A332001 Number of compositions (ordered partitions) of n into distinct parts that do not divide n. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A337697 A328599

Adjacent sequences:  A331998 A331999 A332000 * A332002 A332003 A332004

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 04 2020

STATUS

approved

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Last modified June 14 01:29 EDT 2021. Contains 345016 sequences. (Running on oeis4.)