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A210560 Triangle of coefficients of polynomials v(n,x) jointly generated with A210559; see the Formula section.

%I A210560 #5 Mar 30 2012 18:58:16
%S A210560 1,3,1,5,4,2,7,9,9,3,9,16,23,16,5,11,25,46,48,30,8,13,36,80,110,101,
%T A210560 54,13,15,49,127,215,257,203,97,21,17,64,189,378,552,570,401,172,34,
%U A210560 19,81,268,616,1057,1337,1228,776,303,55,21,100,366,948,1862,2772
%N A210560 Triangle of coefficients of polynomials v(n,x) jointly generated with A210559; see the Formula section.
%C A210560 Column 1: odd positive integers (A005408)
%C A210560 Column 2: squares (A000290)
%C A210560 Row n ends with F(n), where F=A000045 (Fibonacci numbers)
%C A210560 Row sums: A005409
%C A210560 Alternating row sums: 1,2,3,4,5,6,7,8,...(A000027)
%C A210560 For a discussion and guide to related arrays, see A208510.
%F A210560 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210560 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210560 where u(1,x)=1, v(1,x)=1.
%e A210560 First five rows:
%e A210560 1
%e A210560 3...1
%e A210560 5...4...2
%e A210560 7...9...9...3
%e A210560 9...16...23...16...5
%e A210560 First three polynomials v(n,x): 1, 3 + x , 5 + 4x + 2x^2.
%t A210560 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210560 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210560 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210560 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210560 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210560 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210560 TableForm[cu]
%t A210560 Flatten[%]  (* A210559 *)
%t A210560 Table[Expand[v[n, x]], {n, 1, z}]
%t A210560 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210560 TableForm[cv]
%t A210560 Flatten[%]  (* A210560 *)
%Y A210560 Cf. A210559, A208510.
%K A210560 nonn,tabl
%O A210560 1,2
%A A210560 _Clark Kimberling_, Mar 22 2012