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%I #13 Nov 16 2014 15:01:18
%S 1,2,4,7,14,30,62,124,247,495,994,1999,4020,8076,16204,32482,65076,
%T 130326,260927,522298,1045325,2091849,4185665,8374551,16754372,
%U 33517355,67048754,134120372,268277888,536615992,1073329437,2146816436,4293887542,8588186785
%N Number of compositions of n such that the number of parts and the smallest part are coprime.
%H Alois P. Heinz, <a href="/A199888/b199888.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A000079(n-1) - A199889(n).
%e a(4) = 7: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1], [4].
%p b:= proc(n, t, g) option remember;
%p `if`(n=0, `if`(igcd(g, t)=1, 1, 0),
%p add(b(n-i, t+1, min(i, g)), i=1..n))
%p end:
%p a:= n-> b(n, 0, infinity):
%p seq(a(n), n=1..40);
%t 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_ *)
%Y Cf. A000079, A199889, A200928.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Nov 11 2011
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