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A060920 Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros). 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

Companion triangle (odd-indexed members) A060921.

LINKS

Table of n, a(n) for n=0..46.

Yidong Sun, Numerical Triangles and Several Classical Sequences, Fib. Quart. 43, no. 4, Nov. 2005, pp. 359-370.

FORMULA

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); otherwise 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_{m=0..n} A061176(n, m)*x^m (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

EXAMPLE

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

CROSSREFS

Sequence in context: A209148 A126124 A123971 * A107842 A126216 A124733

Adjacent sequences:  A060917 A060918 A060919 * A060921 A060922 A060923

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 20 2001

STATUS

approved

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)