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A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section.

%I A210741 #5 Mar 30 2012 18:58:17
%S A210741 1,1,3,1,5,8,1,7,19,21,1,9,34,65,55,1,11,53,141,210,144,1,13,76,257,
%T A210741 534,654,377,1,15,103,421,1111,1905,1985,987,1,17,134,641,2041,4447,
%U A210741 6512,5911,2584,1,19,169,925,3440,9038,16837,21557,17345,6765,1
%N A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section.
%C A210741 Rows end with even-indexed Fibonacci numbers
%C A210741 Row sums: A007070
%C A210741 Alternating row sums:  signed powers of 2
%C A210741 For a discussion and guide to related arrays, see A208510.
%F A210741 u(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A210741 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210741 where u(1,x)=1, v(1,x)=1.
%e A210741 First five rows:
%e A210741 1
%e A210741 1...3
%e A210741 1...5...8
%e A210741 1...7...19...21
%e A210741 1...9...34...65...55
%e A210741 First three polynomials u(n,x): 1, 1+ 3x, 1 + 5x + 8x^2.
%t A210741 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210741 u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210741 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210741 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210741 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210741 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210741 TableForm[cu]
%t A210741 Flatten[%]     (* A210741 *)
%t A210741 Table[Expand[v[n, x]], {n, 1, z}]
%t A210741 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210741 TableForm[cv]
%t A210741 Flatten[%]     (* A210742 *)
%Y A210741 Cf. A210742, A208510.
%K A210741 nonn,tabl
%O A210741 1,3
%A A210741 _Clark Kimberling_, Mar 24 2012