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A199888 Number of compositions of n such that the number of parts and the smallest part are coprime. 3
1, 2, 4, 7, 14, 30, 62, 124, 247, 495, 994, 1999, 4020, 8076, 16204, 32482, 65076, 130326, 260927, 522298, 1045325, 2091849, 4185665, 8374551, 16754372, 33517355, 67048754, 134120372, 268277888, 536615992, 1073329437, 2146816436, 4293887542, 8588186785 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..500

FORMULA

a(n) = A000079(n-1) - A199889(n).

EXAMPLE

a(4) = 7: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1], [4].

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..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, Min[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, Infinity]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Nov 05 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A000079, A199889, A200928.

Sequence in context: A293336 A321401 A000671 * A157133 A202850 A247295

Adjacent sequences:  A199885 A199886 A199887 * A199889 A199890 A199891

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 11 2011

STATUS

approved

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Last modified September 26 06:05 EDT 2020. Contains 337346 sequences. (Running on oeis4.)