%I #4 Mar 30 2012 18:58:16
%S 1,3,6,3,11,10,6,19,27,23,12,32,62,73,52,24,53,132,193,187,116,48,87,
%T 266,468,552,462,256,96,142,517,1061,1482,1495,1112,560,192,231,978,
%U 2297,3688,4369,3896,2624,1216,384,375,1813,4797,8703,11758
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section.
%C Row sums: 3^(n-1)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3
%e 6....3
%e 11...10...6
%e 19...27...23...12
%e First three polynomials u(n,x): 1, 3, 6 + 3x.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*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[%] (* A210201 *)
%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[%] (* A210202 *)
%Y Cf. A210202, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 18 2012
|