This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A212388 Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 8). 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24312, 48648, 92721, 170811, 311886, 589590, 1220979, 2864973, 7450852, 20309628, 55305706, 146505451, 373452808, 913836082, 2150455648, 4887179761, 10794337952, 23375638064, 50219351232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Lengths of descents are unrestricted. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..750 Vaclav Kotesovec, Asymptotic of subsequences of A212382 FORMULA G.f. satisfies: A(x) = 1+x*A(x)/(1-(x*A(x))^8). a(n) ~ s^2 / (n^(3/2) * r^(n-1/2) * sqrt(2*Pi*p*(s-1)*(1+s/(1+p*(s-1))))), where p = 8 and r = 0.4098875088359862102..., s = 1.880071788712472133... are roots of the system of equations r = p*(s-1)^2 / (s*(1-p+p*s)), (r*s)^p = (s-1-r*s)/(s-1). - Vaclav Kotesovec, Jul 16 2014 EXAMPLE a(0) = 1: the empty path. a(1) = 1: UD. a(9) = 2: UDUDUDUDUDUDUDUDUD, UUUUUUUUUDDDDDDDDD. a(10) = 11: UDUDUDUDUDUDUDUDUDUD, UDUUUUUUUUUDDDDDDDDD, UUUUUUUUUDDDDDDDDDUD, UUUUUUUUUDDDDDDDDUDD, UUUUUUUUUDDDDDDDUDDD, UUUUUUUUUDDDDDDUDDDD, UUUUUUUUUDDDDDUDDDDD, UUUUUUUUUDDDDUDDDDDD, UUUUUUUUUDDDUDDDDDDD, UUUUUUUUUDDUDDDDDDDD, UUUUUUUUUDUDDDDDDDDD. 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)^8), A), x, n+1), x, n): seq(a(n), n=0..40); CROSSREFS Column k=8 of A212382. Sequence in context: A115205 A306753 A306860 * A198769 A037554 A106804 Adjacent sequences:  A212385 A212386 A212387 * A212389 A212390 A212391 KEYWORD nonn AUTHOR Alois P. Heinz, May 12 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 19 06:59 EDT 2019. Contains 322237 sequences. (Running on oeis4.)