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Search: id:A125171
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| A125171 |
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Riordan array ((1-x)/(1-3x+x^2),x/(1-x)) read by rows. |
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+0
2
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| 1, 2, 1, 5, 3, 1, 13, 8, 4, 1, 34, 21, 12, 5, 1, 89, 55, 33, 17, 5, 1, 233, 144, 88, 50, 23, 7, 1, 610, 377, 232, 138, 73, 30, 8, 1, 1597, 987, 609, 370, 211, 103, 38, 9, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partial column sums triangle of odd indexed Fibonacci numbers.
Left border = odd indexed Fibonacci numbers, next-to-left border = even indexed Fibonacci numbers. Row sums = A061667: (1, 3, 9, 26, 73, 201...).
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FORMULA
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Let the left border = odd indexed Fibonacci numbers, (1, 2, 5, 13, 34...); then for k>1, T(n,k) = (n-1,k) + (n-1,k-1).
G.f.: (1-x)^2/((1-3x+x^2)(1-x(1+y)). - Paul Barry (pbarry(AT)wit.ie), Dec 05 2006
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EXAMPLE
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(6,3) = 33 = 12 + 21 = (5,3) + (5,2). First few rows of the triangle are:
1;
2, 1;
5, 3, 1;
13, 8, 4, 1;
34, 21, 12, 5, 1;
89, 55, 33, 17, 6, 1;
...
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CROSSREFS
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Cf. A125171.
Sequence in context: A106513 A054446 A047858 this_sequence A048472 A038622 A112339
Adjacent sequences: A125168 A125169 A125170 this_sequence A125172 A125173 A125174
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 22 2006
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EXTENSIONS
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New description from Paul Barry, Dec 05 2006
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