A337902 The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (2,1).

3, 50, 735, 10584, 152460, 2208492, 32207175, 472780880, 6982113996, 103673813880, 1546866469148, 23179817220000, 348690679038000, 5263441096145400, 79698007774092375, 1210159553338375200, 18422202264818467500, 281089726445607849000

Offset: 1

Author

R. J. Mathar, Sep 29 2020

Keywords

• nonn
• easy
• walk

Examples

			a(1)=3 represents 3 walks of length 3: RRU, URR and RUR.
		

Crossrefs

Cf. A002894 (at (0,0)), A060150 (at (1,0)), A135389 (at (1,1)), A337900 (at (2,0)), A337901 (at (3,0))

Formula

a(n) = binomial(2*n+1,n-1)*binomial(2*n+1,n) = A002054(n)*A001700(n).

G.f.: 3*x*3F2(2,5/2,5/2; 3,4; 16*x).

D-finite with recurrence (n-1)*(n+2)*(n+1)*a(n) -4*n*(2*n+1)^2*a(n-1)=0.

A135389(n) = 2*A060150(n+1) +2*a(n).