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