A328460 Number of compositions of n with no part divisible by the next.

1, 1, 1, 2, 2, 4, 5, 8, 11, 16, 26, 35, 53, 76, 115, 168, 244, 363, 528, 782, 1144, 1685, 2474, 3633, 5347, 7844, 11539, 16946, 24919, 36605, 53782, 79053, 116142, 170700, 250800, 368585, 541610, 795884, 1169572, 1718593, 2525522, 3711134, 5453542, 8013798, 11776138

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Example

The a(1) = 1 through a(9) = 16 compositions:
  (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)     (9)
            (21)  (31)  (23)  (42)   (25)   (35)    (27)
                        (32)  (51)   (34)   (53)    (45)
                        (41)  (231)  (43)   (62)    (54)
                              (321)  (52)   (71)    (63)
                                     (61)   (251)   (72)
                                     (232)  (323)   (81)
                                     (421)  (341)   (234)
                                            (431)   (252)
                                            (521)   (342)
                                            (2321)  (351)
                                                    (423)
                                                    (432)
                                                    (531)
                                                    (621)
                                                    (3231)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; Divisible[y, x]]&]], {n, 0, 10}]

Prog

(PARI) seq(n)={my(r=matid(n)); for(k=1, n, for(i=1, k-1, r[i, k]=sum(j=1, k-i, if(j%i, r[j, k-i])))); concat([1], vecsum(Col(r)))} \\ Andrew Howroyd, Oct 19 2019

Crossrefs

The case of partitions is A328171.

If we also require no part to be divisible by the prior, we get A328508.

Compositions with each part relatively prime to the next are A167606.

Compositions with no part relatively prime to the next are A178470.

Cf. A328026, A328028, A328161, A328172, A328189.

Sequence in context: A089299 A017910 A240734 * A238478 A013979 A107458

Adjacent sequences: A328457 A328458 A328459 * A328461 A328462 A328463

Keyword

nonn

Author

Gus Wiseman, Oct 17 2019

Extensions

Terms a(26) and beyond from Andrew Howroyd, Oct 19 2019

Status

approved