The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328598 Number of compositions of n with no part circularly followed by a divisor. 12
 1, 0, 0, 0, 0, 2, 0, 4, 2, 7, 12, 11, 22, 26, 55, 63, 99, 149, 215, 324, 458, 699, 1006, 1492, 2185, 3202, 4734, 6928, 10242, 14951, 22023, 32365, 47557, 69905, 102633, 150983, 221712, 325918, 478841, 703647, 1034103, 1519431, 2233061, 3281003, 4821790, 7085358 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A composition of n is a finite sequence of positive integers summing to n. Circularity means the last part is followed by the first. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 FORMULA a(n > 0) = A318726(n) - 1. EXAMPLE The a(5) = 2 through a(12) = 22 compositions (empty column not shown):   (2,3)  (2,5)  (3,5)  (2,7)    (3,7)      (2,9)    (5,7)   (3,2)  (3,4)  (5,3)  (4,5)    (4,6)      (3,8)    (7,5)          (4,3)         (5,4)    (6,4)      (4,7)    (2,3,7)          (5,2)         (7,2)    (7,3)      (5,6)    (2,7,3)                        (2,4,3)  (2,3,5)    (6,5)    (3,2,7)                        (3,2,4)  (2,5,3)    (7,4)    (3,4,5)                        (4,3,2)  (3,2,5)    (8,3)    (3,5,4)                                 (3,5,2)    (9,2)    (3,7,2)                                 (5,2,3)    (2,4,5)  (4,3,5)                                 (5,3,2)    (4,5,2)  (4,5,3)                                 (2,3,2,3)  (5,2,4)  (5,3,4)                                 (3,2,3,2)           (5,4,3)                                                     (7,2,3)                                                     (7,3,2)                                                     (2,3,2,5)                                                     (2,3,4,3)                                                     (2,5,2,3)                                                     (3,2,3,4)                                                     (3,2,5,2)                                                     (3,4,3,2)                                                     (4,3,2,3)                                                     (5,2,3,2) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@Not/@Divisible@@@Partition[#, 2, 1, 1]&]], {n, 0, 10}] PROG (PARI) b(n, q, pred)={my(M=matrix(n, n)); for(k=1, n, M[k, k]=pred(q, k); for(i=1, k-1, M[i, k]=sum(j=1, k-i, if(pred(j, i), M[j, k-i], 0)))); M[q, ]} seq(n)={concat([1], sum(k=1, n, b(n, k, (i, j)->i%j<>0)))} \\ Andrew Howroyd, Oct 26 2019 CROSSREFS The necklace version is A328600, or A318729 without singletons. The version with singletons is A318726. The non-circular version is A328460. Also forbidding parts circularly followed by a multiple gives A328599. Partitions with no part followed by a divisor are A328171. Cf. A000740, A008965, A167606, A178470, A318748, A328187, A328508, A328593, A328597, A328601, A328603, A328609. Sequence in context: A285348 A163123 A194346 * A284010 A278082 A327442 Adjacent sequences:  A328595 A328596 A328597 * A328599 A328600 A328601 KEYWORD nonn AUTHOR Gus Wiseman, Oct 24 2019 EXTENSIONS Terms a(26) and beyond from Andrew Howroyd, Oct 26 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)