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A199885 Number of compositions of n such that the greatest part is not divisible by the number of parts. 2
0, 1, 1, 6, 10, 23, 49, 106, 215, 444, 906, 1849, 3759, 7621, 15402, 31091, 62676, 126206, 253860, 510204, 1024665, 2056608, 4125625, 8272436, 16580967, 33223336, 66550937, 133278720, 266857006, 534220745, 1069297319, 2140037990, 4282507048, 8569103770 (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^(n+1)-x)^d-(x^n-x)^d)/(x-1)^d).
a(n) = A000079(n-1) - A171632(n).
EXAMPLE
a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1].
MAPLE
b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(g, t)=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[g, t] == 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: A079426 A212161 A132994 * A024499 A143236 A107306
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved

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Last modified March 4 12:45 EST 2024. Contains 370532 sequences. (Running on oeis4.)