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A210550 Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.

%I A210550 #8 Mar 30 2012 18:58:16
%S A210550 1,2,2,2,6,4,2,7,16,8,2,7,23,40,16,2,7,24,71,96,32,2,7,24,81,207,224,
%T A210550 64,2,7,24,82,266,575,512,128,2,7,24,82,279,843,1535,1152,256,2,7,24,
%U A210550 82,280,939,2572,3967,2560,512,2,7,24,82,280,955,3102,7565,9983
%N A210550 Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.
%C A210550 Row sums: -1+odd-indexed Fibonacci numbers
%C A210550 For a discussion and guide to related arrays, see A208510.
%F A210550 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210550 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1
%F A210550 where u(1,x)=1, v(1,x)=1.
%e A210550 First five rows:
%e A210550 2
%e A210550 2...2
%e A210550 2...6...4
%e A210550 2...7...16....8
%e A210550 2...7...28....40...16
%e A210550 First three polynomials v(n,x): 2, 2 + 2x , 2 + 6x + 4x^2.
%t A210550 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210550 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210550 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210550 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210550 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210550 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210550 TableForm[cu]
%t A210550 Flatten[%]    (* A210549 *)
%t A210550 Table[Expand[v[n, x]], {n, 1, z}]
%t A210550 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210550 TableForm[cv]
%t A210550 Flatten[%]    (* A210550 *)
%Y A210550 Cf. A210549, A208510.
%K A210550 nonn,tabl
%O A210550 1,2
%A A210550 _Clark Kimberling_, Mar 22 2012