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A328508
Number of compositions of n with no part divisible by the next or the prior.
10
1, 1, 1, 1, 1, 3, 1, 6, 4, 8, 14, 14, 27, 30, 55, 69, 97, 155, 200, 312, 421, 630, 893, 1260, 1864, 2600, 3813, 5395, 7801, 11196, 15971, 23126, 32917, 47514, 67993, 97670, 140334, 200913, 289147, 414119, 595109, 853751, 1225086, 1759405, 2523151, 3623984, 5198759
OFFSET
0,6
LINKS
EXAMPLE
The a(1) = 1 through a(11) = 14 compositions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(23) (25) (35) (27) (37) (29)
(32) (34) (53) (45) (46) (38)
(43) (323) (54) (64) (47)
(52) (72) (73) (56)
(232) (234) (235) (65)
(252) (253) (74)
(432) (325) (83)
(343) (92)
(352) (254)
(523) (272)
(532) (353)
(2323) (434)
(3232) (452)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; Divisible[y, x]||Divisible[x, y]]&]], {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(i%j && 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 only forbid parts to be divisible by the next, we get A328460.
Compositions with each part relatively prime to the next are A167606.
Compositions with no part relatively prime to the next are A178470.
Sequence in context: A193864 A066840 A127754 * A210841 A007383 A206434
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 17 2019
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, Oct 19 2019
STATUS
approved