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A241691
Number of Carlitz compositions of n with exactly one descent.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 27 2014
STATUS
approved