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Search: id:A104698
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| A104698 |
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Triangle read by rows: T(n,k)=sum{j=0..n-k, C(k,j)C(n-j+1,n-k-j). |
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3
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| 1, 2, 1, 3, 4, 1, 4, 9, 6, 1, 5, 16, 19, 8, 1, 6, 25, 44, 33, 10, 1, 7, 36, 85, 96, 51, 12, 1, 8, 49, 146, 225, 180, 73, 14, 1
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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The triangle is extracted from the product A * B; A = [1; 1, 1; 1, 1, 1;...], B = [1; 1, 1; 1, 3, 1; 1, 5, 5, 1;...] both infinite lower triangular matrices (rest of the terms are zeros). The triangle of matrix B by rows = A008288, Delannoy numbers.
Riordan array (1/(1-x)^2, x(1+x)/(1-x))=(1/(1-x), x)*(1/(1-x), x(1+x)/(1-x)); T(n, k)=sum{j=0..n, sum{i=0..j-k, C(j-k, i)C(k, i)2^i}}; T(n, k)=sum{j=0..k, sum{i=n-k-j, (n-k-j-i+1)*C(k, j)C(k+i-1, i)}}; - Paul Barry (pbarry(AT)wit.ie), Jul 18 2005
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EXAMPLE
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The first few rows are:
1;
2, 1;
3, 4, 1;
4, 9, 6, 1;
5, 16, 19, 8, 1;
6, 25, 44, 33, 10, 1;
7, 36, 85, 96, 51, 12, 1;
...
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CROSSREFS
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Column 3 = A005900, column 4 = A014820. Row sums = A048739, partial sums of Pell numbers: 1, 3, 8, 20, 49, 119...
Diagonal sums are A008937(n+1).
Cf. A048739, A008288, A005900, A014820.
Adjacent sequences: A104695 A104696 A104697 this_sequence A104699 A104700 A104701
Sequence in context: A133807 A093375 A103283 this_sequence A067066 A125103 A107616
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2005
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