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A199884 Number of compositions of n such that the number of parts is not divisible by the greatest part. 2
0, 1, 1, 6, 8, 19, 43, 90, 167, 339, 722, 1503, 2987, 5883, 11820, 24167, 49348, 99707, 199626, 398475, 797457, 1604029, 3237867, 6534327, 13143278, 26336266, 52664325, 105349525, 211135006, 423949168, 851981311, 1711365899, 3433202397, 6878160656, 13768314357 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
G.f.: Sum_{n>0} (2^(n-1)*x^n -Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n).
a(n) = A000079(n-1) - A171634(n).
EXAMPLE
a(5) = 8: [1,2,2], [1,4], [2,1,2], [2,2,1], [2,3], [3,2], [4,1], [5].
MAPLE
b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=0, 0, 1), add(b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n, 0, 0): seq(a(n), n=1..40);
MATHEMATICA
b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[Mod[t, g] == 0, 0, 1], Sum [b[n-i, t+1, Max[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 05 2014, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A173975 A349770 A349225 * A028331 A279729 A357946
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved

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Last modified March 4 15:47 EST 2024. Contains 370532 sequences. (Running on oeis4.)