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.

1, 0, 2, 4, 9, 21, 46, 98, 213, 459, 979, 2082, 4408, 9294, 19535, 40937, 85561, 178392, 371131, 770556, 1596936, 3303986, 6825163, 14078718, 29002331, 59670920, 122627798, 251735331, 516247636, 1057687986, 2165046327, 4428017780, 9049083763, 18478717262

Offset

5,3

Links

Alois P. Heinz, Table of n, a(n) for n = 5..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, 5) -b(n, 0, 4):
seq(a(n), n=5..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, 5] - b[n, 0, 4];
Table[a[n], {n, 5, 50}] (* Jean-François Alcover, May 21 2018, after Alois P. Heinz *)

Crossrefs

Column k=5 of A091613.

Sequence in context: A035056 A332800 A093698 * A061439 A351644 A027711

Adjacent sequences: A091616 A091617 A091618 * A091620 A091621 A091622

Keyword

nonn

Author

Christian G. Bower, Jan 23 2004

Status

approved