cp's OEIS Frontend

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.

%I A318748 #16 Nov 04 2019 10:39:48
%S A318748 1,1,2,4,7,13,24,43,82,151,285,535,1005,1883,3533,6631,12460,23407,
%T A318748 43952,82538,154999,291088,546674,1026687,1928118,3621017,6800300,
%U A318748 12771086,23984329,45042959,84591339,158863807,298348613,560303342,1052258402,1976157510
%N 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.
%H A318748 Andrew Howroyd, <a href="/A318748/b318748.txt">Table of n, a(n) for n = 0..200</a>
%F A318748 a(n) = A328609(n) + 1 for n > 1. - _Andrew Howroyd_, Nov 01 2019
%e A318748 The a(5) = 13 compositions with adjacent parts coprime:
%e A318748   (5)
%e A318748   (41) (14) (32) (23)
%e A318748   (311) (131) (113)
%e A318748   (2111) (1211) (1121) (1112)
%e A318748   (11111)
%e A318748 Missing from this list are (221), (212), and (122).
%t A318748 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Or[Length[#]==1,And@@CoprimeQ@@@Partition[#,2,1,1]]&]],{n,20}]
%o A318748 (PARI)
%o A318748 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, ]}
%o A318748 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
%Y A318748 Cf. A000740, A008965, A059966, A100953, A167606, A296302, A318726, A318727, A318728, A318745, A328609.
%K A318748 nonn
%O A318748 0,3
%A A318748 _Gus Wiseman_, Sep 02 2018
%E A318748 a(21)-a(35) from _Alois P. Heinz_, Sep 02 2018
%E A318748 Name corrected by _Gus Wiseman_, Nov 04 2019