A091620 - OEIS

%I #10 May 21 2018 03:22:08

%S 1,0,2,4,9,20,45,98,210,453,971,2068,4387,9275,19545,41064,86055,

%T 179913,375338,781497,1624250,3370238,6982398,14445576,29846586,

%U 61591860,126956859,261411737,537723480,1105055809,2268948882,4654815069,9541957646,19545570684

%N 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 Alois P. Heinz, <a href="/A091620/b091620.txt">Table of n, a(n) for n = 6..1000</a>

%p b:= proc(n, l, k) option remember; `if`(n=0, 1, add(`if`(

%p       i=l, 0, add(b(n-i*j, i, k), j=1..min(k, n/i))), i=1..n))

%p     end:

%p a:= n-> b(n, 0, 6) -b(n, 0, 5):

%p seq(a(n), n=6..50);  # _Alois P. Heinz_, Feb 08 2017

%t 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 a[n_] := b[n, 0, 6] - b[n, 0, 5];

%t Table[a[n], {n, 6, 50}] (* _Jean-François Alcover_, May 21 2018, after _Alois P. Heinz_ *)

%Y Column k=6 of A091613.

%K nonn

%O 6,3

%A _Christian G. Bower_, Jan 23 2004