The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A176697 G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^2. 3
 1, 1, 3, 7, 20, 63, 208, 711, 2496, 8944, 32578, 120263, 448938, 1691776, 6427130, 24589043, 94653498, 366344216, 1424750506, 5565002716, 21821377624, 85867522754, 338974659036, 1342074448663, 5327845401606, 21203102693634, 84574191671494, 338060063747476 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A recursive sequence of vectors: a(n) = vector(a(0),...,a(n-1)) * Reverse(vector(a(0),...,a(n-1)) with a(0) = a(1) = 1, a(2) = 3. Number of Schroeder paths in which horizontal sequences are always exactly HH and never precede an up step. - David Scambler, May 23 2012 REFERENCES F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 231. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: A(x) = (1 - sqrt(1 - 4*x*(1+x^2)))/(2*x). [Paul D. Hanna, Nov 12 2011] a(n) = Sum_{i=1..n} a(i-1)*a(n-i) for n>2; a(0) = a(1) = 1, a(2) = 3. - Alois P. Heinz, May 24 2012 Recurrence: (n+1)*a(n) = 2*(2*n-1)*a(n-1) + 2*(2*n-7)*a(n-3). - Vaclav Kotesovec, Sep 11 2013 a(n) ~ sqrt(3-8*z)/(4*sqrt(Pi)*n^(3/2)*z^(n+1)), where z = (9+sqrt(273))^(1/3)/(2*3^(2/3)) - 2/(3*(9+sqrt(273)))^(1/3) = 0.236732903864563... is the root of the equation 4*z*(1+z^2)=1. - Vaclav Kotesovec, Sep 11 2013 a(n) = sum(m=0..n/2, binomial(n-2*m+1,m)*binomial(2*(n-2*m),n-2*m)/(n+1-2*m)). - Vladimir Kruchinin, Nov 21 2014 MAPLE a:= proc(n) a(n):= add(a(i-1)*a(n-i), i=1..n) end: a(0), a(1), a(2):= 1, 1, 3: seq(a(n), n=0..30); # Alois P. Heinz, May 24 2012 MATHEMATICA a[0] := 1; a[1] := 1; a[2] := 3; a[n_] := a[n] = Table[a[i], {i, 0, n - 1}].Table[a[n - 1 - i], {i, 0, n - 1}]; Table[a[n], {n, 0, 30}] f[x_, y_, d_]:=f[x, y, d] = If[x<0||y

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

Last modified June 2 14:40 EDT 2023. Contains 363097 sequences. (Running on oeis4.)