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A199886 Number of compositions of n such that the number of parts and the greatest part are coprime. 3
1, 2, 2, 7, 7, 18, 40, 85, 148, 285, 584, 1231, 2516, 5069, 10175, 20306, 40000, 78328, 154233, 307586, 620903, 1262129, 2566697, 5193429, 10424746, 20761986, 41131719, 81358316, 161239595, 320900400, 641688619, 1287937462, 2589941043, 5208522925, 10461756080 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A000079(n-1) - A199887(n).
EXAMPLE
a(5) = 7: [1,1,1,1,1], [1,2,2], [2,1,2], [2,2,1], [2,3], [3,2], [5].
MAPLE
b:= proc(n, t, g) option remember;
`if`(n=0, `if`(igcd(g, t)=1, 1, 0),
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 [GCD[g, t] == 1, 1, 0], 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: A318086 A244049 A271229 * A117779 A300952 A195326
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)