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A241693
Number of Carlitz compositions of n with exactly three descents.
2
3, 11, 31, 78, 175, 363, 715, 1342, 2421, 4237, 7208, 11971, 19473, 31083, 48787, 75437, 115046, 173263, 257972, 380039, 554400, 801452, 1148805, 1633699, 2306108, 3232635, 4501745, 6230400, 8572442, 11729536, 15965001, 21621202, 29141879, 39100192, 52233835
OFFSET
9,1
COMMENTS
No two adjacent parts of a Carlitz composition are equal.
LINKS
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, 4), polynom))
end:
a:= n-> coeff(b(n, 0), x, 3):
seq(a(n), n=9..50);
CROSSREFS
Column k=3 of A241701.
Sequence in context: A245931 A190590 A341705 * A087323 A236752 A034543
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 27 2014
STATUS
approved