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A210213 Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section.

%I A210213 #4 Mar 30 2012 18:58:16
%S A210213 1,2,1,4,3,1,7,9,4,1,12,21,16,5,1,20,46,46,25,6,1,33,94,121,85,36,7,1,
%T A210213 54,185,289,260,141,49,8,1,88,353,653,708,491,217,64,9,1,143,659,1409,
%U A210213 1800,1499,847,316,81,10,1,232,1209,2939,4320,4229,2863,1366
%N A210213 Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section.
%C A210213 Row sums:  even-indexed Fibonacci numbers
%C A210213 For a discussion and guide to related arrays, see A208510.
%F A210213 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210213 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210213 where u(1,x)=1, v(1,x)=1.
%e A210213 First five rows:
%e A210213 1
%e A210213 2....1
%e A210213 4....3....1
%e A210213 7....9....4....1
%e A210213 12...21...16...5...1
%e A210213 First three polynomials u(n,x): 1, 2 + x, 4 + 3x + x^2.
%t A210213 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210213 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210213 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210213 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210213 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210213 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210213 TableForm[cu]
%t A210213 Flatten[%]    (* A210213 *)
%t A210213 Table[Expand[v[n, x]], {n, 1, z}]
%t A210213 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210213 TableForm[cv]
%t A210213 Flatten[%]    (* A210214 *)
%Y A210213 Cf. A210214, A208510.
%K A210213 nonn,tabl
%O A210213 1,2
%A A210213 _Clark Kimberling_, Mar 19 2012