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 A212389 Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 9). 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 12, 67, 287, 1002, 3004, 8009, 19449, 43759, 92380, 184787, 353137, 650497, 1170632, 2110021, 3977161, 8271836, 19536661, 51111062, 140210129, 385123916, 1032218316, 2670065961, 6645249777, 15922990909, 36823807747, 82485177457 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS Lengths of descents are unrestricted. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..800 FORMULA G.f. satisfies: A(x) = 1+x*A(x)/(1-(x*A(x))^9). EXAMPLE a(0) = 1: the empty path. a(1) = 1: UD. a(10) = 2: UDUDUDUDUDUDUDUDUDUD, UUUUUUUUUUDDDDDDDDDD. a(11) = 12: UDUDUDUDUDUDUDUDUDUDUD, UDUUUUUUUUUUDDDDDDDDDD, UUUUUUUUUUDDDDDDDDDDUD, UUUUUUUUUUDDDDDDDDDUDD, UUUUUUUUUUDDDDDDDDUDDD, UUUUUUUUUUDDDDDDDUDDDD, UUUUUUUUUUDDDDDDUDDDDD, UUUUUUUUUUDDDDDUDDDDDD, UUUUUUUUUUDDDDUDDDDDDD, UUUUUUUUUUDDDUDDDDDDDD, UUUUUUUUUUDDUDDDDDDDDD, UUUUUUUUUUDUDDDDDDDDDD. MAPLE b:= proc(x, y, u) option remember;       `if`(x<0 or  y b(n\$2, true): seq (a(n), n=0..40); # second Maple program a:= n-> coeff(series(RootOf(A=1+x*A/(1-(x*A)^9), A), x, n+1), x, n): seq (a(n), n=0..40); CROSSREFS Column k=9 of A212382. Sequence in context: A197745 A039633 A180195 * A020062 A185035 A185235 Adjacent sequences:  A212386 A212387 A212388 * A212390 A212391 A212392 KEYWORD nonn AUTHOR Alois P. Heinz, May 12 2012 STATUS approved

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