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A091619 Number of compositions (ordered partitions) of n such that some part is repeated consecutively 5 times and no part is repeated consecutively more than 5 times.

%I A091619 #11 May 21 2018 05:14:44
%S A091619 1,0,2,4,9,21,46,98,213,459,979,2082,4408,9294,19535,40937,85561,
%T A091619 178392,371131,770556,1596936,3303986,6825163,14078718,29002331,
%U A091619 59670920,122627798,251735331,516247636,1057687986,2165046327,4428017780,9049083763,18478717262
%N A091619 Number of compositions (ordered partitions) of n such that some part is repeated consecutively 5 times and no part is repeated consecutively more than 5 times.
%H A091619 Alois P. Heinz, <a href="/A091619/b091619.txt">Table of n, a(n) for n = 5..1000</a>
%p A091619 b:= proc(n, l, k) option remember; `if`(n=0, 1, add(`if`(
%p A091619       i=l, 0, add(b(n-i*j, i, k), j=1..min(k, n/i))), i=1..n))
%p A091619     end:
%p A091619 a:= n-> b(n, 0, 5) -b(n, 0, 4):
%p A091619 seq(a(n), n=5..50);  # _Alois P. Heinz_, Feb 08 2017
%t A091619 b[n_, l_, k_] := b[n, l, k] = If[n == 0, 1, Sum[If[i == l, 0, Sum[b[n - i*j, i, k], {j, 1, Min[k, n/i]}]], {i, 1, n}]];
%t A091619 a[n_] := b[n, 0, 5] - b[n, 0, 4];
%t A091619 Table[a[n], {n, 5, 50}] (* _Jean-François Alcover_, May 21 2018, after _Alois P. Heinz_ *)
%Y A091619 Column k=5 of A091613.
%K A091619 nonn
%O A091619 5,3
%A A091619 _Christian G. Bower_, Jan 23 2004