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).

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

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