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Search: id:A038792
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| A038792 |
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Array defined by T(i,1)=T(1,j)=1, T(i,j)=Max(T(i-1,j)+T(i-1,j-1); T(i-1,j-1)+T(i,j-1)) read by antidiagonals. |
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+0
13
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 5, 8, 8, 5, 1, 1, 6, 12, 13, 12, 6, 1, 1, 7, 17, 21, 21, 17, 7, 1, 1, 8, 23, 33, 34, 33, 23, 8, 1, 1, 9, 30, 50, 55, 55, 50, 30, 9, 1, 1, 10, 38, 73, 88, 89, 88, 73, 38, 10, 1, 1, 11, 47, 103, 138, 144, 144
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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A path-counting array, read by rows: for 0<=j<=i, T(i,j)=number of paths from (0,0) to (i-j,j) using steps (1 unit right) or (1 unit up and 1 unit right); for j>i, T(i,j)=T(i,i-j)=number of paths from (0,0) to (i-j,j) using steps (1 up) or (1 up and 1 right).
Row sums: A029907.
Central numbers T(2n,n)=A001519(n) for n >= 1 (odd-indexed Fibonacci numbers).
T(2n+1,n)=A001906(n) for n >= 0 (even-indexed Fibonacci numbers).
T(2n+2,n)=A027941(n); T(2n+3,n)=A054452(n).
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FORMULA
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T(i, 0)=T(i, i)=1 for i >= 0; T(2, 1)=2; T(i, j)=T(i-1, j)+T(i-2, j-1), T(i, i-j)=T(i, j) for 2<=j<=i/2, i >= 3.
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EXAMPLE
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Rows: {1}; {1,1}; {1,2,1}; {1,3,3,1}; {1,4,5,4,1}; ...
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CROSSREFS
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Sequence in context: A077028 A114225 A072704 this_sequence A046688 A067049 A090641
Adjacent sequences: A038789 A038790 A038791 this_sequence A038793 A038794 A038795
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), May 02 2000
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EXTENSIONS
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New description from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2003
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