A241691 Number of Carlitz compositions of n with exactly one descent.

1, 2, 4, 8, 13, 21, 33, 50, 73, 106, 150, 209, 289, 393, 529, 707, 935, 1227, 1601, 2072, 2666, 3413, 4344, 5501, 6937, 8707, 10883, 13554, 16815, 20787, 25617, 31465, 38532, 47056, 57302, 69596, 84320, 101907, 122875, 147833, 177471, 212608, 254201, 303335

Offset: 3

Author

Alois P. Heinz, Apr 27 2014

Keywords

• nonn

Comments

No two adjacent parts of a Carlitz composition are equal.

Examples

			a(3) = 1: [2,1].
a(4) = 2: [3,1], [1,2,1].
a(5) = 4: [4,1], [3,2], [2,1,2], [1,3,1].
a(6) = 8: [4,2], [5,1], [3,1,2], [1,3,2], [1,4,1], [2,3,1], [2,1,3], [1,2,1,2].
a(7) = 13: [4,3], [6,1], [5,2], [2,1,4], [4,1,2], [1,4,2], [2,3,2], [3,1,3], [1,5,1], [2,4,1], [1,2,3,1], [1,3,1,2], [1,2,1,3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Column k=1 of A241701.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
       convert(series(add(`if`(i=j, 0, b(n-j, j)*
      `if`(j coeff(b(n, 0), x, 1):
seq(a(n), n=3..50);