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%I #5 Oct 02 2013 16:26:13
%S 1,0,3,0,4,7,0,2,14,17,0,2,12,46,41,0,2,8,54,140,99,0,2,8,42,212,408,
%T 239,0,2,8,34,200,758,1154,577,0,2,8,34,160,866,2544,3194,1393,0,2,8,
%U 34,144,754,3448,8154,8696,3363,0,2,8,34,144,642,3400,12850
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.
%C Leading coefficient of u(n,x): A001333
%C Limiting row: 0,2,8,34,144,610,...(Fibonacci numbers)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=x*u(n-1,x)+2x*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First six rows:
%e 1
%e 0...3
%e 0...4...7
%e 0...2...14...17
%e 0...2...12...46...41
%e 0...2...8....54...140...99
%e First three polynomials u(n,x): 1, 3x, 4x + 7x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210878 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210879 *)
%Y Cf. A210879, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 30 2012
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