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Search: id:A113413
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| A113413 |
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A Riordan array of coordination sequences. |
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+0
4
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| 1, 2, 1, 2, 4, 1, 2, 8, 6, 1, 2, 12, 18, 8, 1, 2, 16, 38, 32, 10, 1, 2, 20, 66, 88, 50, 12, 1, 2, 24, 102, 192, 170, 72, 14, 1, 2, 28, 146, 360, 450, 292, 98, 16, 1, 2, 32, 198, 608, 1002, 912, 462, 128, 18, 1, 2, 36, 258, 952, 1970, 2364, 1666, 688, 162, 20, 1, 2, 40, 326
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Columns include A040000,A008574,A005899,A008412,A008413,A008414. Row sums are A078057(n)=A001333(n+1). Diagonal sums are A001590(n+3). Reverse of A035607. Signed version is A080246. Inverse is A080245.
For another version see A122542. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 15 2006
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FORMULA
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Riordan array ((1+x)/(1-x), x(1+x)/(1-x)); T(n, k)=sum{i=0..n-k, C(k+1, i)C(n-i, k)}; T(n, k)=sum{j=0..n-k, C(k+j, j)C(k+1, n-k-j)}; T(n, k)=D(n, k)+D(n-1, k) where D(n, k)=sum{j=0..n-k, C(n-k, j)C(k, j)2^j}=A008288(n, k); T(n, k)=T(n-1, k)+T(n-1, k-1)+T(n-2, k-1);
T(n, k)=sum{j=0..n, C(floor((n+j)/2), k)C(k, floor((n-j)/2))}; - Paul Barry (pbarry(AT)wit.ie), Nov 13 2005
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EXAMPLE
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Triangle begins
1;
2, 1;
2, 4, 1;
2, 8, 6, 1;
2, 12, 18, 8, 1;
2, 16, 38, 32, 10, 1;
2, 20, 66, 88, 50, 12, 1;
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CROSSREFS
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Sequence in context: A114791 A129994 A080246 this_sequence A125694 A136678 A110162
Adjacent sequences: A113410 A113411 A113412 this_sequence A113414 A113415 A113416
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 29 2005
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