cp's OEIS Frontend

A318727 Number of integer compositions of n where adjacent parts are indivisible (either way) and the last and first part are also indivisible (either way).

%I A318727 #12 Sep 08 2018 17:03:02
%S A318727 1,1,1,1,3,1,5,3,5,13,9,23,15,37,45,63,115,131,207,265,415,603,823,
%T A318727 1251,1673,2521,3519,5147,7409,10449,15225,21497,31285,44719,64171,
%U A318727 92315,131619,190085,271871,391189,560979,804265,1155977,1656429,2381307,3414847
%N A318727 Number of integer compositions of n where adjacent parts are indivisible (either way) and the last and first part are also indivisible (either way).
%H A318727 Andrew Howroyd, <a href="/A318727/b318727.txt">Table of n, a(n) for n = 1..200</a>
%e A318727 The a(10) = 13 compositions:
%e A318727   (10)
%e A318727   (7,3) (3,7) (6,4) (4,6)
%e A318727   (5,3,2) (5,2,3) (3,5,2) (3,2,5) (2,5,3) (2,3,5)
%e A318727   (3,2,3,2) (2,3,2,3)
%t A318727 Table[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,({___,x_,y_,___}/;Divisible[x,y]||Divisible[y,x])|({y_,___,x_}/;Divisible[x,y]||Divisible[y,x])]&]//Length,{n,20}]
%o A318727 (PARI)
%o A318727 b(n,k,pred)={my(M=matrix(n,n)); for(n=1, n, M[n,n]=pred(k,n); for(j=1, n-1, M[n,j]=sum(i=1, n-j, if(pred(i,j), M[n-j,i], 0)))); sum(i=1, n, if(pred(i,k), M[n,i], 0))}
%o A318727 a(n)={1 + sum(k=1, n-1, b(n-k, k, (i,j)->i%j<>0&&j%i<>0))} \\ _Andrew Howroyd_, Sep 08 2018
%Y A318727 Cf. A000740, A008965, A167606, A285573, A296302, A303362, A304713, A316476, A318726.
%K A318727 nonn
%O A318727 1,5
%A A318727 _Gus Wiseman_, Sep 02 2018
%E A318727 a(21)-a(28) from _Robert Price_, Sep 07 2018
%E A318727 Terms a(29) and beyond from _Andrew Howroyd_, Sep 08 2018