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A210188 Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.

%I A210188 #4 Mar 30 2012 18:58:16
%S A210188 1,2,2,3,7,2,4,16,11,2,5,30,36,15,2,6,50,91,64,19,2,7,77,196,204,100,
%T A210188 23,2,8,112,378,540,385,144,27,2,9,156,672,1254,1210,650,196,31,2,10,
%U A210188 210,1122,2640,3289,2366,1015,256,35,2,11,275,1782,5148,8008
%N A210188 Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.
%C A210188 Row sums:  -1+(odd-indexed Fibonacci numbers): 1,4,12,...
%C A210188 Period of alternating row sums: (1,-,-2,-3,-2,0)
%C A210188 For a discussion and guide to related arrays, see A208510.
%F A210188 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210188 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210188 where u(1,x)=1, v(1,x)=1.
%e A210188 First five rows:
%e A210188 1
%e A210188 2...2
%e A210188 3...7....2
%e A210188 4...16...11...2
%e A210188 5...30...36...15...2
%e A210188 First three polynomials v(n,x): 1, 2 + 2x , 3 + 7x + 2x^2.
%t A210188 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210188 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210188 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210188 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210188 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210188 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210188 TableForm[cu]
%t A210188 Flatten[%]    (* A210187 *)
%t A210188 Table[Expand[v[n, x]], {n, 1, z}]
%t A210188 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210188 TableForm[cv]
%t A210188 Flatten[%]    (* A210188 *)
%Y A210188 Cf. A210187, A208510.
%K A210188 nonn,tabl
%O A210188 1,2
%A A210188 _Clark Kimberling_, Mar 18 2012