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A062105
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Number of ways a pawn-like piece (with the initial 2-step move forbidden and starting from any square on the back rank) can end at various squares on infinite chess board.
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2
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1, 1, 2, 1, 3, 5, 1, 3, 8, 13, 1, 3, 9, 22, 35, 1, 3, 9, 26, 61, 96, 1, 3, 9, 27, 75, 171, 267, 1, 3, 9, 27, 80, 216, 483, 750, 1, 3, 9, 27, 81, 236, 623, 1373, 2123, 1, 3, 9, 27, 81, 242, 694, 1800, 3923, 6046, 1, 3, 9, 27, 81, 243, 721, 2038, 5211, 11257, 17303, 1, 3, 9, 27
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Table formatted as a square array shows the top-left corner of the infinite board.
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LINKS
| Hans L. Bodlaender, The Chess Variant Pages
Hans L. Bodlaender et al., editors, The Piececlopedia (An overview of several fairy chess pieces)
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MAPLE
| [seq(CPTVSeq(j), j=0..91)]; CPTVSeq := n -> ChessPawnTriangleV( (2+(n-((trinv(n)*(trinv(n)-1))/2))), ((((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1) );
ChessPawnTriangleV := 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; RETURN(ChessPawnTriangleV(r-1, c-1)+ChessPawnTriangleV(r-1, c)+ChessPawnTriangleV(r-1, c+1)); end;
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PROG
| (PARI) T(n, k)=if(n<1|k<1, 0, if(n==1, 1, T(n-1, k-1)+T(n-1, k)+T(n-1, k+1)))
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CROSSREFS
| A005773 gives the left column of the table. A000244 (powers of 3) gives the diagonal of the table. Variant of A062104. Cf. also A062103.
Sequence in context: A130466 A129322 A089984 * A093412 A119355 A076110
Adjacent sequences: A062102 A062103 A062104 * A062106 A062107 A062108
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KEYWORD
| nonn,tabl
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AUTHOR
| Antti Karttunen May 30 2001
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