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A210236 Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section.

%I A210236 #4 Mar 30 2012 18:58:16
%S A210236 1,3,2,6,8,3,11,22,16,4,19,52,57,28,5,32,112,166,124,45,6,53,228,428,
%T A210236 432,241,68,7,87,446,1018,1300,984,432,98,8,142,848,2285,3540,3397,
%U A210236 2036,728,136,9,231,1578,4912,8964,10443,7962,3914,1168,183,10
%N A210236 Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section.
%C A210236 Row sums: powers of 3
%C A210236 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,...
%C A210236 For a discussion and guide to related arrays, see A208510.
%F A210236 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210236 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1
%F A210236 where u(1,x)=1, v(1,x)=1.
%e A210236 First five rows:
%e A210236 1
%e A210236 3....2
%e A210236 6....8....3
%e A210236 11...22...16...4
%e A210236 19...52...57...28...5
%e A210236 First three polynomials v(n,x): 1, 3 + 2x , 6 + 8x + 3x^2.
%t A210236 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210236 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210236 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210236 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210236 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210236 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210236 TableForm[cu]
%t A210236 Flatten[%]      (* A210235 *)
%t A210236 Table[Expand[v[n, x]], {n, 1, z}]
%t A210236 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210236 TableForm[cv]
%t A210236 Flatten[%]      (* A210236 *)
%Y A210236 Cf. A210235, A208510.
%K A210236 nonn,tabl
%O A210236 1,2
%A A210236 _Clark Kimberling_, Mar 20 2012