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A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section.

%I A210217 #4 Mar 30 2012 18:58:16
%S A210217 1,2,1,2,5,1,2,6,12,1,2,6,19,27,1,2,6,20,57,58,1,2,6,20,67,160,121,1,
%T A210217 2,6,20,68,218,424,248,1,2,6,20,68,231,680,1073,503,1,2,6,20,68,232,
%U A210217 775,2028,2619,1014,1,2,6,20,68,232,791,2543,5797,6214,2037,1,2
%N A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section.
%C A210217 Limiting row:  A006012
%C A210217 Row sums: even-indexed Fibonacci numbers: 1,3,8,21,...
%C A210217 For a discussion and guide to related arrays, see A208510.
%F A210217 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210217 v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A210217 where u(1,x)=1, v(1,x)=1.
%e A210217 First five rows:
%e A210217 1
%e A210217 2...1
%e A210217 2...5...1
%e A210217 2...6...12...1
%e A210217 2...6...19...27...1
%e A210217 First three polynomials u(n,x): 1, 2 + x, 2 + 5x + x^2.
%t A210217 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210217 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210217 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210217 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210217 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210217 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210217 TableForm[cu]
%t A210217 Flatten[%]    (* A210217 *)
%t A210217 Table[Expand[v[n, x]], {n, 1, z}]
%t A210217 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210217 TableForm[cv]
%t A210217 Flatten[%]     (* A210218 *)
%Y A210217 Cf. A210218, A208510.
%K A210217 nonn,tabl
%O A210217 1,2
%A A210217 _Clark Kimberling_, Mar 19 2012