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.

1, 0, 2, 4, 9, 20, 45, 98, 210, 453, 971, 2068, 4387, 9275, 19545, 41064, 86055, 179913, 375338, 781497, 1624250, 3370238, 6982398, 14445576, 29846586, 61591860, 126956859, 261411737, 537723480, 1105055809, 2268948882, 4654815069, 9541957646, 19545570684

Offset

6,3

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Maple

b:= proc(n, l, k) option remember; `if`(n=0, 1, add(`if`(
      i=l, 0, add(b(n-i*j, i, k), j=1..min(k, n/i))), i=1..n))
    end:
a:= n-> b(n, 0, 6) -b(n, 0, 5):
seq(a(n), n=6..50);  # Alois P. Heinz, Feb 08 2017

Mathematica

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}]];
a[n_] := b[n, 0, 6] - b[n, 0, 5];
Table[a[n], {n, 6, 50}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A091613.

Sequence in context: A360871 A199296 A219229 * A208738 A144686 A108469

Adjacent sequences: A091617 A091618 A091619 * A091621 A091622 A091623

Keyword

nonn

Author

Christian G. Bower, Jan 23 2004

Status

approved