0,3

Number of square lattice walks that start at (0,0) and end at (1,0) after 2n-1 steps, free to pass through (1,0) at intermediate steps. - S. R. Finch (Steven.Finch(AT)inria.fr), Dec 20 2001

Number of paths of length n connecting two neighboring nodes in optimal chordal graph of degree 4, G(2*d(G)^2+2*d(G)+1,2d(G)+1), of diameter d(G). - B. Dubalski (dubalski(AT)atr.bydgoszcz.pl), Feb 05 2002

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 1994 Addison-Wesley company, Inc.

A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (5.1.29.2)

K. A. Ross and C. R. B. Wright, Discrete Mathematics, 1992 Prentice Hall Inc.

Harry J. Smith, Table of n, a(n) for n=0,...,200

R. Bacher, Meander algebras

G.f.: 1+(1/AGM(1, sqrt(1-16*x))-1)/4. - Michael Somos, Dec 12, 2002

G.f. = 1+(K(16x)-1)/4 = 1+Sum_{k>0} q^k/(1+q^(2k)) where K(16x) is complete Elliptic integral of first kind at 16x=k^2 and q is the nome. - Michael Somos, May 09, 2005

E.g.f. Sum_{n>0} a(n)*x^(2n-1)/(2n-1)! = BesselI(0, 2x)*BesselI(1, 2x) . - Michael Somos Jun 22 2005

a(n)=(n*C(n-1)/2)^2; for n = 1, 3, 5, ..., 2*d(G)-1; when n even a(n)=0; C - Catalan number - B. Dubalski (dubalski(AT)atr.bydgoszcz.pl), Feb 05 2002

a(9)=9^2*C(4)=9^2*14^2=15876

(PARI) a(n)=if(n<1, n==0, binomial(2*n-1, n-1)^2)

(PARI) { for (n=0, 200, if (n==0, a=1, a=binomial(2*n - 1, n - 1)^2); write("b060150.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 02 2009]

a(n)=A002894(n)/4, n>0.

Adjacent sequences: A060147 A060148 A060149 this_sequence A060151 A060152 A060153

Sequence in context: A065736 A092936 A056002 this_sequence A103461 A101563 A007133

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), Apr 10 2001