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A060920 Bisection of Fibonacci triangle A037027: even indexed members of column sequences of A037027 (not counting leading zeros). 9

%I

%S 1,2,1,5,5,1,13,20,9,1,34,71,51,14,1,89,235,233,105,20,1,233,744,942,

%T 594,190,27,1,610,2285,3522,2860,1295,315,35,1,1597,6865,12473,12402,

%U 7285,2534,490,44,1,4181,20284

%N Bisection of Fibonacci triangle A037027: even indexed members of column sequences of A037027 (not counting leading zeros).

%C Row sums give A007583. Column sequences (without leading zeros) give for m=0..5: A001519, A054444, A061178-81.

%C Companion triangle (odd indexed members) A060921.

%H Yidong Sun, <a href="http://www.fq.math.ca/Papers1/43-4/paper43-4-10b.pdf">Numerical Triangles and Several Classical Sequences</a>, Fib. Quart. 43, no. 4, Nov. 2005, pp. 359-370.

%F T(n, m) = A037027(2*n-m, m).

%F 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.

%F 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).

%F G.f.: (1-x*(1+y))/(1-(3+2*y)*x+(1+y)^2*x^2). - _Vladeta Jovovic_, Oct 11 2003

%e {1}; {2,1}; {5,5,1}; {13,20,9,1}; ...; pFe(2,x)=1-x+x^2.

%K nonn,easy,tabl

%O 0,2

%A _Wolfdieter Lang_, Apr 20 2001

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Last modified December 13 05:16 EST 2018. Contains 318082 sequences. (Running on oeis4.)