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URL: https://oeis.org/A199889

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A199889
Number of compositions of n such that the number of parts and the smallest part are not coprime.
3
0, 0, 0, 1, 2, 2, 2, 4, 9, 17, 30, 49, 76, 116, 180, 286, 460, 746, 1217, 1990, 3251, 5303, 8639, 14057, 22844, 37077, 60110, 97356, 157568, 254920, 412387, 667212, 1079754, 1747807, 2829756, 4582021, 7419619, 12014143, 19452288, 31492382, 50979547, 82517631
OFFSET
1,5
LINKS
FORMULA
a(n) = A000079(n-1) - A199888(n).
a(n) ~ 1/(2*sqrt(5)) * ((1+sqrt(5))/2)^(n-1). - Vaclav Kotesovec, May 01 2014
EXAMPLE
a(8) = 4: [2,2,2,2], [2,6], [4,4], [6,2].
MAPLE
b:= proc(n, t, g) option remember;
`if`(n=0, `if`(igcd(g, t)<>1, 1, 0),
add(b(n-i, t+1, min(i, g)), i=1..n))
end:
a:= n-> b(n, 0, infinity):
seq(a(n), n=1..50);
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, Min[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, Infinity]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 05 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved