The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A199890 Number of compositions of n such that the number of parts and the largest part and the smallest part are pairwise coprime. 2

%I #14 Nov 16 2014 15:06:09

%S 1,1,1,6,4,15,37,81,133,270,565,1200,2449,4961,10014,20083,39585,

%T 77566,152934,305587,617857,1257333,2558837,5180712,10404918,20732162,

%U 41087390,81291644,161136101,320733232,641408052,1287453960,2589099670,5207066575,10459270462

%N Number of compositions of n such that the number of parts and the largest part and the smallest part are pairwise coprime.

%H Alois P. Heinz, <a href="/A199890/b199890.txt">Table of n, a(n) for n = 1..250</a>

%e a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1].

%p b:= proc(n, t, g, k) option remember;

%p `if`(n=0, `if`(igcd(g, t)=1 and igcd(k, t)=1 and igcd(g, k)=1, 1, 0),

%p add(b(n-i, t+1, max(i, g), min(i, k)), i=1..n))

%p end:

%p a:= n-> b(n, 0, 0, infinity):

%p seq(a(n), n=1..40);

%t b[n_, t_, g_, k_] := b[n, t, g, k] = If[n == 0, If[GCD[g, t] == 1 && GCD[k, t] == 1 && GCD[g, k] == 1, 1, 0], Sum[b[n-i, t+1, Max[i, g], Min[i, k]], {i, 1, n}]]; a[n_] := b[n, 0, 0, Infinity]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Nov 05 2014, after _Alois P. Heinz_ *)

%Y Cf. A201218.

%K nonn

%O 1,4

%A _Alois P. Heinz_, Nov 11 2011

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

Last modified December 11 10:38 EST 2023. Contains 367722 sequences. (Running on oeis4.)