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Search: id:A027011
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| A027011 |
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Triangular array T read by rows: T(n,k)=t(n,2k+1) for 0<=k<=[ (2n-1)/2 ], t given by A027960, n >= 0. |
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18
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| 3, 3, 4, 3, 7, 5, 3, 7, 15, 6, 3, 7, 18, 28, 7, 3, 7, 18, 44, 47, 8, 3, 7, 18, 47, 98, 73, 9, 3, 7, 18, 47, 120, 199, 107, 10, 3, 7, 18, 47, 123, 291, 373, 150, 11, 3, 7, 18, 47, 123, 319, 661, 654, 203, 12, 3, 7, 18, 47, 123, 322, 806, 1404, 1085, 267, 13, 3, 7, 18, 47
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Right-edge columns are polynomials approximating Lucas(2n).
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FORMULA
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T(n, k) = Lucas(2n) = A005248(n) for 2k+1<=n, otherwise the (2n-2k+1)th coefficient of the power series for (1+2x)/{(1-x-x^2)(1-x)^(2k-n+1)}.
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EXAMPLE
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...........................3
.........................3,4
.......................3,7,5
....................3,7,15,6
.................3,7,18,28,7
..............3,7,18,44,47,8
...........3,7,18,47,98,73,9
....3,7,18,47,120,199,107,10
3,7,18,47,123,291,373,150,11
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CROSSREFS
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This is a bisection of the "Lucas array " A027960, see A026998 for the other bisection.
Right-edge columns include A027965, A027967, A027969, A027971.
An earlier version of this entry had (unjustifiably) each row starting with 1.
Sequence in context: A029882 A083503 A062069 this_sequence A061023 A057690 A090972
Adjacent sequences: A027008 A027009 A027010 this_sequence A027012 A027013 A027014
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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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