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A210564 Triangle of coefficients of polynomials v(n,x) jointly generated with A210563; see the Formula section.

%I A210564 #5 Mar 30 2012 18:58:17
%S A210564 1,2,3,2,7,8,2,8,22,21,2,8,29,67,55,2,8,30,101,200,144,2,8,30,111,341,
%T A210564 588,377,2,8,30,112,404,1122,1708,987,2,8,30,112,417,1442,3613,4913,
%U A210564 2584,2,8,30,112,418,1543,5044,11425,14018,6765,2,8,30,112,418
%N A210564 Triangle of coefficients of polynomials v(n,x) jointly generated with A210563; see the Formula section.
%C A210564 Last terms in rows: even-indexed Fibonacci numbers
%C A210564 Limiting row:  A052530
%C A210564 For a discussion and guide to related arrays, see A208510.
%F A210564 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210564 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210564 where u(1,x)=1, v(1,x)=1.
%e A210564 First five rows:
%e A210564 1
%e A210564 2...3
%e A210564 2...7...8
%e A210564 2...8...22...21
%e A210564 2...8...29...67...55
%e A210564 First three polynomials v(n,x): 1, 2 + 3x , 2 + 8x + 22x^2.
%t A210564 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210564 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210564 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210564 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210564 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210564 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210564 TableForm[cu]
%t A210564 Flatten[%]  (* A210563 *)
%t A210564 Table[Expand[v[n, x]], {n, 1, z}]
%t A210564 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210564 TableForm[cv]
%t A210564 Flatten[%]  (* A210564 *)
%Y A210564 Cf. A210563, A208510.
%K A210564 nonn,tabl
%O A210564 1,2
%A A210564 _Clark Kimberling_, Mar 23 2012