A005569 Number of walks on square lattice.

4, 34, 308, 3024, 31680, 349206, 4008004, 47530912, 579058896, 7215393640, 91644262864, 1183274479040, 15497363512800, 205519758825150, 2755739674246500, 37314861293793600, 509727100259638800

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• R. K. Guy, Letter to N. J. A. Sloane, May 1990
• R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6.

Programs

PARI

a(n)=4*if(n<2,n==1,a(n-1)*n*(2*n-1)*(2*n+1)*(5*n+7)/((n-1)*(n+2)*(n+3)*(5*n+2)))

Formula

G.f.: 4_F_3 ( [ 2, 17/5, 5/2, 3/2 ]; [ 4, 5, 12/5 ];16 x ).

a(n)(n-1)(n+2)(n+3)(5n+2) = a(n-1)4n(2n-1)(2n+1)(5n+7), n>1. - Michael Somos, Mar 04 2003