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A209572 Triangle of coefficients of polynomials v(n,x) jointly generated with A209571; see the Formula section.

%I A209572 #5 Mar 30 2012 18:58:15
%S A209572 1,1,3,1,3,5,1,3,11,7,1,3,11,29,9,1,3,11,41,61,11,1,3,11,41,129,111,
%T A209572 13,1,3,11,41,153,339,183,15,1,3,11,41,153,523,771,281,17,1,3,11,41,
%U A209572 153,571,1571,1569,409,19,1,3,11,41,153,571,2035,4161,2929,571,21
%N A209572 Triangle of coefficients of polynomials v(n,x) jointly generated with A209571; see the Formula section.
%C A209572 Combinatorial limit of row n satisfies linear recurrence
%C A209572 r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=3.  For a
%C A209572 discussion and guide to related arrays, see A208510.
%F A209572 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209572 v(n,x)=2x*u(n-1,x)+x*v(n-1,x) +1,
%F A209572 where u(1,x)=1, v(1,x)=1.
%e A209572 First five rows:
%e A209572 1
%e A209572 1...3
%e A209572 1...3...5
%e A209572 1...3...11...7
%e A209572 1...3...11...29...9
%e A209572 First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 5x^2.
%t A209572 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209572 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209572 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209572 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209572 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209572 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209572 TableForm[cu]
%t A209572 Flatten[%]   (* A209571 *)
%t A209572 Table[Expand[v[n, x]], {n, 1, z}]
%t A209572 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209572 TableForm[cv]
%t A209572 Flatten[%]   (* A209572 *)
%Y A209572 Cf. A209571, A208510.
%K A209572 nonn,tabl
%O A209572 1,3
%A A209572 _Clark Kimberling_, Mar 11 2012