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Search: id:A026998
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| A026998 |
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Triangular array T read by rows: T(n,k)=t(n,2k), t given by A027960, 0<=k<=n, n >= 0. |
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20
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| 1, 1, 1, 1, 4, 1, 1, 4, 8, 1, 1, 4, 11, 13, 1, 1, 4, 11, 26, 19, 1, 1, 4, 11, 29, 54, 26, 1, 1, 4, 11, 29, 73, 101, 34, 1, 1, 4, 11, 29, 76, 171, 174, 43, 1, 1, 4, 11, 29, 76, 196, 370, 281, 53, 1, 1, 4, 11, 29, 76, 199, 487, 743, 431, 64, 1, 1, 4
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Right-edge columns are polynomials approximating Lucas(2n+1).
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FORMULA
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T(n, k) = Lucas(2n+1) = A002878(n) for 2k<=n, otherwise the (2n-2k)th coefficient of the power series for (1+2x)/{(1-x-x^2)(1-x)^(2k-n)}.
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EXAMPLE
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............................1
..........................1,1
........................1,4,1
......................1,4,8,1
..................1,4,11,13,1
...............1,4,11,26,19,1
............1,4,11,29,54,26,1
........1,4,11,29,73,101,34,1
....1,4,11,29,76,171,174,43,1
1,4,11,29,76,196,370,281,53,1
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CROSSREFS
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This is a bisection of the "Lucas array" A027960, see A027011 for the other bisection.
Row sums are in A000918. Right-edge columns include A034856, A027966, A027968, A027970, A027972.
Sequence in context: A091570 A116669 A016523 this_sequence A080061 A124258 A001638
Adjacent sequences: A026995 A026996 A026997 this_sequence A026999 A027000 A027001
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), May 05 2005
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