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A062103
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Number of paths by which an unpromoted knight (keima) of Shogi can move to various squares on infinite board, if it starts from its origin square, the second leftmost square of the back rank.
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4
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0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 14
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OFFSET
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1,20
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COMMENTS
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Table formatted as a square array shows the top-left corner of the infinite board. This is an aerated and sligthly skewed variant of Catalan's triangle A009766.
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LINKS
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Table of n, a(n) for n=1..104.
Hans L. Bodlaender, The Chess Variant Pages
Fairbairn, Leggett et al., Information about Shogi (Japanese chess)
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MAPLE
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[seq(ShoogiKnightSeq(j), j=1..120)]; ShoogiKnightSeq := n -> ShoogiKnightTriangle(trinv(n-1)-1, (n-((trinv(n-1)*(trinv(n-1)-1))/2))-1);
ShoogiKnightTriangle := proc(r, m) option remember; if(m < 0) then RETURN(0); fi; if(r < 0) then RETURN(0); fi; if(m > r) then RETURN(0); fi; if((1 = r) and (0 = m)) then RETURN(1); fi; RETURN(ShoogiKnightTriangle(r-3, m-2) + ShoogiKnightTriangle(r-1, m-2)); end;
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CROSSREFS
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A009766, A049604, A062104, trinv given at A054425.
Sequence in context: A181009 A056626 A091398 * A112314 A104261 A028702
Adjacent sequences: A062100 A062101 A062102 * A062104 A062105 A062106
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen May 30 2001
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STATUS
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approved
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