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Search: id:A062104
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| A062104 |
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Number of ways a black pawn (starting at any square on the second back rank) can (theoretically) end at various squares on infinite chess board. |
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5
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| 0, 0, 1, 0, 1, 2, 0, 1, 3, 6, 0, 1, 3, 9, 15, 0, 1, 3, 10, 25, 40, 0, 1, 3, 10, 29, 69, 109, 0, 1, 3, 10, 30, 84, 193, 302, 0, 1, 3, 10, 30, 89, 242, 544, 846, 0, 1, 3, 10, 30, 90, 263, 698, 1544, 2390, 0, 1, 3, 10, 30, 90, 269, 774, 2016, 4406, 6796, 0, 1, 3, 10, 30, 90, 270
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Table formatted as a square array shows the top-left corner of the infinite board.
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MAPLE
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[seq(CPTSeq(j), j=0..91)]; CPTSeq := n -> ChessPawnTriangle( (1+(n-((trinv(n)*(trinv(n)-1))/2))), ((((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1) );
ChessPawnTriangle := proc(r, c) option remember; if(r < 2) then RETURN(0); fi; if(c < 1) then RETURN(0); fi; if(2 = r) then RETURN(1); fi; if(4 = r) then RETURN(1+ChessPawnTriangle(r-1, c-1)+ChessPawnTriangle(r-1, c)+ChessPawnTriangle(r-1, c+1));
else RETURN(ChessPawnTriangle(r-1, c-1)+ChessPawnTriangle(r-1, c)+ChessPawnTriangle(r-1, c+1)); fi; end;
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CROSSREFS
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A062106 gives the left column and A062107 the diagonal of the table. A062105 is a more regular variant. Cf. also A062103. trinv given at A054425.
Sequence in context: A134405 A091612 A108458 this_sequence A018843 A072737 A061290
Adjacent sequences: A062101 A062102 A062103 this_sequence A062105 A062106 A062107
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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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