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Rectangular array T(n,k) read by antidiagonals; generating function of column n is 1/F(n,x), where F(n,x) is the polynomial 1 - x - x^2 - 2*x^3 -...- F(n+1)*x^n and F(n+1) is the (n+1)st Fibonacci number, for n=0,1,2,...
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%I #3 Mar 30 2012 18:57:05

%S 1,1,1,1,1,1,1,1,2,1,1,1,2,3,1,1,1,2,5,5,1,1,1,2,5,9,8,1,1,1,2,5,12,

%T 18,13,1,1,1,2,5,12,24,37,21,1,1,1,2,5,12,29,52,73,34,1,1,1,2,5,12,29,

%U 62,115,146,55,1,1,1,2,5,12,29,70,140,251,293,89,1,1,1,2,5,12,29,70,156

%N Rectangular array T(n,k) read by antidiagonals; generating function of column n is 1/F(n,x), where F(n,x) is the polynomial 1 - x - x^2 - 2*x^3 -...- F(n+1)*x^n and F(n+1) is the (n+1)st Fibonacci number, for n=0,1,2,...

%C Transpose of the array in A096669.

%e Rows

%e 1 1 1 1 1

%e 1 1 1 1 1

%e 1 2 2 2 2

%e 1 3 5 5 5

%e 1 5 9 12 12

%e Column 0 has g.f. 1/(1-x)

%e Column 1 has g.f. 1/(1-x-x^2)

%e Column 2 has g.g. 1/(1-x-x^2-2*x^3).

%Y Cf. A000045, A096669, A000129.

%K nonn,tabl

%O 1,9

%A _Clark Kimberling_, Jul 03 2004