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A318726
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Number of integer compositions of n that have only one part or whose consecutive parts are indivisible and the last and first part are also indivisible.
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13
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1, 1, 1, 1, 3, 1, 5, 3, 8, 13, 12, 23, 27, 56, 64, 100, 150, 216, 325, 459, 700, 1007, 1493, 2186, 3203, 4735, 6929, 10243, 14952, 22024, 32366, 47558, 69906, 102634, 150984, 221713, 325919, 478842, 703648, 1034104, 1519432, 2233062, 3281004, 4821791, 7085359
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OFFSET
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1,5
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LINKS
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FORMULA
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EXAMPLE
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The a(10) = 13 compositions:
(10)
(7,3) (3,7) (6,4) (4,6)
(5,3,2) (5,2,3) (3,5,2) (3,2,5) (2,5,3) (2,3,5)
(3,2,3,2) (2,3,2,3)
The a(11) = 12 compositions:
(11)
(9,2) (2,9) (8,3) (3,8) (7,4) (4,7) (6,5) (5,6)
(5,2,4) (4,5,2) (2,4,5)
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MATHEMATICA
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Table[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, ({___, x_, y_, ___}/; Divisible[x, y])|({y_, ___, x_}/; Divisible[x, y])]&]//Length, {n, 20}]
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PROG
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(PARI)
b(n, k, pred)={my(M=matrix(n, n)); for(n=1, n, M[n, n]=pred(k, n); for(j=1, n-1, M[n, j]=sum(i=1, n-j, if(pred(i, j), M[n-j, i], 0)))); sum(i=1, n, if(pred(i, k), M[n, i], 0))}
a(n)={1 + sum(k=1, n-1, b(n-k, k, (i, j)->i%j<>0))} \\ Andrew Howroyd, Sep 08 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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