A337901 The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (3,0).

1, 25, 441, 7056, 108900, 1656369, 25050025, 378224704, 5712638724, 86394844900, 1308887012356, 19868414760000, 302198588499600, 4605510959127225, 70321771565375625, 1075697380745222400, 16483023079048102500, 252980753801047064100, 3888662839165553120100

Offset: 1

Author

R. J. Mathar, Sep 29 2020

Keywords

• nonn
• easy
• walk

Crossrefs

Cf. A002894 (end at (0,0)), A060150 (end at (1,0)), A135389 (end at (1,1)), A337900 (at (2,0)), A337902 (at(2,1))

Formula

a(n) = [A002054(n)]^2.

G.f.: x*4F3(2,2,5/2,5/2; 1,4,4; 16*x).

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