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A318727 Number of integer compositions of n where adjacent parts are indivisible (either way) and the last and first part are also indivisible (either way). 8
1, 1, 1, 1, 3, 1, 5, 3, 5, 13, 9, 23, 15, 37, 45, 63, 115, 131, 207, 265, 415, 603, 823, 1251, 1673, 2521, 3519, 5147, 7409, 10449, 15225, 21497, 31285, 44719, 64171, 92315, 131619, 190085, 271871, 391189, 560979, 804265, 1155977, 1656429, 2381307, 3414847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

EXAMPLE

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)

MATHEMATICA

Table[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, ({___, x_, y_, ___}/; Divisible[x, y]||Divisible[y, x])|({y_, ___, x_}/; Divisible[x, y]||Divisible[y, x])]&]//Length, {n, 20}]

PROG

(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&&j%i<>0))} \\ Andrew Howroyd, Sep 08 2018

CROSSREFS

Cf. A000740, A008965, A167606, A285573, A296302, A303362, A304713, A316476, A318726.

Sequence in context: A091926 A325685 A109606 * A307806 A127418 A099550

Adjacent sequences:  A318724 A318725 A318726 * A318728 A318729 A318730

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 02 2018

EXTENSIONS

a(21)-a(28) from Robert Price, Sep 07 2018

Terms a(29) and beyond from Andrew Howroyd, Sep 08 2018

STATUS

approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)