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A005569 Number of walks on square lattice.
(Formerly M3654)
0
4, 34, 308, 3024, 31680, 349206, 4008004, 47530912, 579058896, 7215393640, 91644262864, 1183274479040, 15497363512800, 205519758825150, 2755739674246500, 37314861293793600, 509727100259638800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

LINKS

Table of n, a(n) for n=1..17.

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.

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

PROG

(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)))

CROSSREFS

Sequence in context: A201684 A155628 A036352 * A232910 A208215 A337390

Adjacent sequences:  A005566 A005567 A005568 * A005570 A005571 A005572

KEYWORD

nonn,walk,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)