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A091620 Number of compositions (ordered partitions) of n such that some part is repeated consecutively 6 times and no part is repeated consecutively more than 6 times.

%I A091620 #10 May 21 2018 03:22:08
%S A091620 1,0,2,4,9,20,45,98,210,453,971,2068,4387,9275,19545,41064,86055,
%T A091620 179913,375338,781497,1624250,3370238,6982398,14445576,29846586,
%U A091620 61591860,126956859,261411737,537723480,1105055809,2268948882,4654815069,9541957646,19545570684
%N A091620 Number of compositions (ordered partitions) of n such that some part is repeated consecutively 6 times and no part is repeated consecutively more than 6 times.
%H A091620 Alois P. Heinz, <a href="/A091620/b091620.txt">Table of n, a(n) for n = 6..1000</a>
%p A091620 b:= proc(n, l, k) option remember; `if`(n=0, 1, add(`if`(
%p A091620       i=l, 0, add(b(n-i*j, i, k), j=1..min(k, n/i))), i=1..n))
%p A091620     end:
%p A091620 a:= n-> b(n, 0, 6) -b(n, 0, 5):
%p A091620 seq(a(n), n=6..50);  # _Alois P. Heinz_, Feb 08 2017
%t A091620 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 A091620 a[n_] := b[n, 0, 6] - b[n, 0, 5];
%t A091620 Table[a[n], {n, 6, 50}] (* _Jean-François Alcover_, May 21 2018, after _Alois P. Heinz_ *)
%Y A091620 Column k=6 of A091613.
%K A091620 nonn
%O A091620 6,3
%A A091620 _Christian G. Bower_, Jan 23 2004