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A272568 Number of distinct n-step paths of a knight moving on an n X n chessboard, starting to at a corner and not visiting any cell twice. 1
0, 0, 2, 20, 256, 2086, 16376, 121418, 871258, 6077730, 41586532, 280783434, 1875742356, 12432917916, 81868580330, 536476588416, 3501125753910, 22778101455784 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..18.

César Eliud Lozada, List of paths for n=1..5

MAPLE

pathCount:=proc(N)

local g1, g2, nStep, gg, nCells, nRow, nCol, nPrev, aNext, nNext, hh, n:

nCells:=N^(2); g1:=[[1]];

for nStep from 1 to N do

g2:=[];

for gg in g1 do

nPrev := gg[-1] ;

nRow:=1+floor((nPrev-1)/(N)); nCol:=1+((nPrev-1) mod N);

aNext:=[];

if nRow-2>=1 then

if nCol-1>=1 then aNext:=[op(aNext), nPrev-2*N-1] fi;

if nCol+1<= N then aNext:=[op(aNext), nPrev-2*N+1] fi;

end if;

if nRow-1>=1 then

if nCol-2>=1 then aNext:=[op(aNext), nPrev-N-2] fi;

if nCol+2<=N then aNext:=[op(aNext), nPrev-N+2] fi;

end if;

if nRow+1<=N then

if nCol-2>=1 then aNext:=[op(aNext), nPrev+N-2] fi;

if nCol+2<=N then aNext:=[op(aNext), nPrev+N+2] fi;

end if;

if nRow+2<=N then

if nCol-1>=1 then aNext:=[op(aNext), nPrev+2*N-1] fi;

if nCol+1<= N then aNext:=[op(aNext), nPrev+2*N+1] fi;

end if;

for nNext in aNext do

if nNext<1 or nNext>nCells or (nNext in gg) then next fi;

g2:=[op(g2), [op(gg), nNext]];

end do:

end do:

g1:=g2;

end do:

#output: comment this block if output is not required

if N>=3 and N<=5 then

hh:=fopen(cat("KnightPaths_", N, ".txt"), WRITE);

for n from 1 to nops(g1) do

fprintf(hh, "%4d: %s\n", n, convert(g1[n], string));

end do:

fclose(hh);

end if;

return nops(g1);

end proc:

lis:=[seq(pathCount(N), N=1..7)];

CROSSREFS

Cf. A272469.

Sequence in context: A099976 A195157 A207151 * A229727 A325409 A155671

Adjacent sequences: A272565 A272566 A272567 * A272569 A272570 A272571

KEYWORD

nonn,walk,more

AUTHOR

César Eliud Lozada, May 02 2016

EXTENSIONS

a(9)-a(15) from Giovanni Resta, May 03 2016

a(16)-a(18) from Bert Dobbelaere, Jan 08 2019

STATUS

approved

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Last modified February 4 23:12 EST 2023. Contains 360082 sequences. (Running on oeis4.)