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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 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.)