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!)
 A318748 Number of integer compositions of n that have only one part or whose consecutive parts are coprime and the last and first part are also coprime. 11
 1, 1, 2, 4, 7, 13, 24, 43, 82, 151, 285, 535, 1005, 1883, 3533, 6631, 12460, 23407, 43952, 82538, 154999, 291088, 546674, 1026687, 1928118, 3621017, 6800300, 12771086, 23984329, 45042959, 84591339, 158863807, 298348613, 560303342, 1052258402, 1976157510 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 FORMULA a(n) = A328609(n) + 1 for n > 1. - Andrew Howroyd, Nov 01 2019 EXAMPLE The a(5) = 13 compositions with adjacent parts coprime:   (5)   (41) (14) (32) (23)   (311) (131) (113)   (2111) (1211) (1121) (1112)   (11111) Missing from this list are (221), (212), and (122). MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Or[Length[#]==1, And@@CoprimeQ@@@Partition[#, 2, 1, 1]]&]], {n, 20}] 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], vector(n, i, i > 1) + sum(k=1, n, b(n, k, (i, j)->gcd(i, j)==1)))} \\ Andrew Howroyd, Nov 01 2019 CROSSREFS Cf. A000740, A008965, A059966, A100953, A167606, A296302, A318726, A318727, A318728, A318745, A328609. Sequence in context: A049285 A002843 A128742 * A107281 A006744 A054175 Adjacent sequences:  A318745 A318746 A318747 * A318749 A318750 A318751 KEYWORD nonn AUTHOR Gus Wiseman, Sep 02 2018 EXTENSIONS a(21)-a(35) from Alois P. Heinz, Sep 02 2018 Name corrected by Gus Wiseman, Nov 04 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 June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)