A091618 Number of compositions (ordered partitions) of n such that some part is repeated consecutively 4 times and no part is repeated consecutively more than 4 times.

1, 0, 2, 4, 10, 22, 46, 101, 218, 466, 991, 2093, 4405, 9232, 19288, 40169, 83416, 172806, 357170, 736710, 1516714, 3117133, 6396116, 13105012, 26814264, 54795330, 111842771, 228030558, 464439943, 945029466, 1921169854, 3902239742, 7919743405, 16061152291

Offset

4,3

Links

Alois P. Heinz, Table of n, a(n) for n = 4..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, 4) -b(n, 0, 3):
seq(a(n), n=4..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, 4] - b[n, 0, 3];
Table[a[n], {n, 4, 50}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *)

Crossrefs

Column k=4 of A091613.

Sequence in context: A369491 A274313 A291397 * A181158 A018108 A033497

Adjacent sequences: A091615 A091616 A091617 * A091619 A091620 A091621

Keyword

nonn

Author

Christian G. Bower, Jan 23 2004

Status

approved