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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Right-edge columns are polynomials approximating Lucas(2n).
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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FORMULA
| 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
| ...........................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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MAPLE
| t:=proc(n, k)option remember:if(k=0 or k=2*n)then return 1:elif(k=1)then return 3:else return t(n-1, k-2) + t(n-1, k-1):fi:end:
T:=proc(n, k)return t(n, 2*k+1):end:
for n from 0 to 8 do for k from 0 to floor((2*n-1)/2) do print(T(n, k)); od:od: # Nathaniel Johnston, Apr 18 2011
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CROSSREFS
| 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: A083503 A062069 A163375 * A174280 A061023 A057690
Adjacent sequences: A027008 A027009 A027010 * A027012 A027013 A027014
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), May 05 2005
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