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A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section.

%I A210743 #5 Mar 30 2012 18:58:17
%S A210743 1,2,3,4,8,7,7,20,25,17,12,43,76,75,41,20,88,194,264,216,99,33,172,
%T A210743 458,770,861,606,239,54,327,1016,2038,2811,2691,1667,577,88,608,2161,
%U A210743 5012,8206,9689,8149,4517,1393,143,1112,4447,11699,22057,30830
%N A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section.
%C A210743 Row n starts with -1+F(n), where F=A000045 (Fibonacci numbers), and ends with A001333(n).  For a discussion and guide to related arrays, see A208510.
%F A210743 u(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210743 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210743 where u(1,x)=1, v(1,x)=1.
%e A210743 First five rows:
%e A210743 1
%e A210743 2....3
%e A210743 4....8....7
%e A210743 7....20...25...17
%e A210743 12...43...76...75...41
%e A210743 First three polynomials u(n,x): 1, 2+ 3x, 4 + 8x + 7x^2.
%t A210743 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210743 u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210743 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210743 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210743 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210743 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210743 TableForm[cu]
%t A210743 Flatten[%]      (* A210743 *)
%t A210743 Table[Expand[v[n, x]], {n, 1, z}]
%t A210743 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210743 TableForm[cv]
%t A210743 Flatten[%]      (* A210744 *)
%Y A210743 Cf. A210744, A208510.
%K A210743 nonn,tabl
%O A210743 1,2
%A A210743 _Clark Kimberling_, Mar 24 2012