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Search: id:A105809
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| A105809 |
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A Fibonacci-Pascal matrix. |
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+0
3
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| 1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 5, 7, 7, 4, 1, 8, 12, 14, 11, 5, 1, 13, 20, 26, 25, 16, 6, 1, 21, 33, 46, 51, 41, 22, 7, 1, 34, 54, 79, 97, 92, 63, 29, 8, 1, 55, 88, 133, 176, 189, 155, 92, 37, 9, 1, 89, 143, 221, 309, 365, 344, 247, 129, 46, 10, 1, 144, 232, 364, 530, 674, 709, 591
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A027934, diagonal sums are A010049(n+1). Inverse is A105810.
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FORMULA
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Riordan array (1/(1-x-x^2), x/(1-x)); Number triangle T(n, k)=sum{j=0..n, binomial(n-j, k+j)}; T(n, 0)=A000045(n), T(n, m)=T(n-1, m-1)+T(n-1, m).
T(n,k)=sum{j=0..n, C(j,n+k-j)}; - Paul Barry (pbarry(AT)wit.ie), Oct 23 2006
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EXAMPLE
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Triangle begins
1;
1,1;
2,2,1;
3,4,3,1;
5,7,7,4,1;
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CROSSREFS
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Sequence in context: A035317 A103923 A061987 this_sequence A091594 A118032 A089692
Adjacent sequences: A105806 A105807 A105808 this_sequence A105810 A105811 A105812
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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), May 04 2005
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