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A005569 Number of walks on square lattice.
(Formerly M3654)
0

%I M3654

%S 4,34,308,3024,31680,349206,4008004,47530912,579058896,7215393640,

%T 91644262864,1183274479040,15497363512800,205519758825150,

%U 2755739674246500,37314861293793600,509727100259638800

%N Number of walks on square lattice.

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

%H R. K. Guy, <a href="/A005555/a005555.pdf">Letter to N. J. A. Sloane, May 1990</a>

%H R. K. Guy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6.

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

%F 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

%o (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)))

%K nonn,walk,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)