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A212369
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Number of Dyck n-paths all of whose ascents and descents have lengths equal to 1 (mod 10).
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 68, 85, 112, 156, 226, 333, 490, 712, 1016, 1421, 1949, 2630, 3512, 4676, 6256, 8464, 11620, 16187, 22811, 32366, 46005, 65225, 91967, 128786, 179140, 247861, 341885, 471332, 651041, 902679
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listen;
history;
text;
internal format)
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OFFSET
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0,12
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f. satisfies: A(x) = 1+A(x)*(x-x^10*(1-A(x))).
a(n) = a(n-1) + Sum_{k=1..n-10} a(k)*a(n-10-k) if n>0; a(0) = 1.
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EXAMPLE
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a(0) = 1: the empty path.
a(1) = 1: UD.
a(11) = 2: UDUDUDUDUDUDUDUDUDUDUD, UUUUUUUUUUUDDDDDDDDDDD.
a(12) = 4: UDUDUDUDUDUDUDUDUDUDUDUD, UDUUUUUUUUUUUDDDDDDDDDDD, UUUUUUUUUUUDDDDDDDDDDDUD, UUUUUUUUUUUDUDDDDDDDDDDD.
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 1, a(n-1) +add(a(k)*a(n-10-k), k=1..n-10))
end:
seq (a(n), n=0..60);
# second Maple program
a:= n-> coeff(series(RootOf(A=1+A*(x-x^10*(1-A)), A), x, n+1), x, n):
seq (a(n), n=0..60);
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CROSSREFS
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Column k=10 of A212363.
Sequence in context: A025739 A000124 A152947 * A212368 A217838 A212367
Adjacent sequences: A212366 A212367 A212368 * A212370 A212371 A212372
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, May 10 2012
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STATUS
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approved
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