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

3,2

Comments

No two adjacent parts of a Carlitz composition are equal.

Links

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

Example

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].

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
       convert(series(add(`if`(i=j, 0, b(n-j, j)*
      `if`(j<i, x, 1)), j=1..n), x, 2), polynom))
    end:
a:= n-> coeff(b(n, 0), x, 1):
seq(a(n), n=3..50);

Crossrefs

Column k=1 of A241701.

Sequence in context: A259964 A218913 A349061 * A164429 A073336 A164420

Adjacent sequences: A241688 A241689 A241690 * A241692 A241693 A241694

Keyword

nonn

Author

Alois P. Heinz, Apr 27 2014

Status

approved