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A060920
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Bisection of Fibonacci triangle A037027: even indexed members of column sequences of A037027 (not counting leading zeros).
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9
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1, 2, 1, 5, 5, 1, 13, 20, 9, 1, 34, 71, 51, 14, 1, 89, 235, 233, 105, 20, 1, 233, 744, 942, 594, 190, 27, 1, 610, 2285, 3522, 2860, 1295, 315, 35, 1, 1597, 6865, 12473, 12402, 7285, 2534, 490, 44, 1, 4181, 20284
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OFFSET
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0,2
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COMMENTS
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Row sums give A007583. Column sequences (without leading zeros) give for m=0..5: A001519, A054444, A061178-81.
Companion triangle (odd indexed members) A060921.
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REFERENCES
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Yidong Sun, Numerical triangles and several classical sequences, Fib. Quart., Nov. 2005, pp. 359-370.
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LINKS
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Table of n, a(n) for n=0..46.
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FORMULA
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T(n, m)= A037027(2*n-m, m).
T(n, m)=((2*(n-m)+1)*A060921(n-1, m-1)+4*n*T(n-1, m-1))/(5*m), n >= m >= 1; T(n, 0) := F(n)^2+F(n+1)^2 = A001519(n), with the Fibonacci numbers F(n)=A000045(n); else 0.
G.f. for column m >= 0: x^m*pFe(m+1, x)/(1-3*x+x^2)^(m+1), where pFe(n, x) := sum(A061176(n, m)*x^m, m=0..n) (row polynomials of signed triangle A061176).
G.f.: (1-x*(1+y))/(1-(3+2*y)*x+(1+y)^2*x^2). - Vladeta Jovovic, Oct 11 2003
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EXAMPLE
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{1}; {2,1}; {5,5,1}; {13,20,9,1}; ...; pFe(2,x)=1-x+x^2.
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CROSSREFS
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Sequence in context: A209164 A209148 A126124 * A107842 A126216 A124733
Adjacent sequences: A060917 A060918 A060919 * A060921 A060922 A060923
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang, Apr 20 2001
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STATUS
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approved
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