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A210195 Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.

%I A210195 #4 Mar 30 2012 18:58:16
%S A210195 1,3,5,4,7,12,8,9,24,32,16,11,40,80,80,32,13,60,160,240,192,64,15,84,
%T A210195 280,560,672,448,128,17,112,448,1120,1792,1792,1024,256,19,144,672,
%U A210195 2016,4032,5376,4608,2304,512,21,180,960,3360,8064,13440,15360
%N A210195 Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.
%C A210195 Row sums:  powers of 3
%C A210195 Periodic alternating row sums: 1,3,1,3,1,3,1,3,...
%C A210195 For a discussion and guide to related arrays, see A208510.
%F A210195 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210195 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A210195 where u(1,x)=1, v(1,x)=1.
%e A210195 First five rows:
%e A210195 1
%e A210195 3
%e A210195 5...4
%e A210195 7...12...8
%e A210195 9...24...32...16
%e A210195 First three polynomials u(n,x): 1, 3, 5 + 4x.
%t A210195 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210195 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210195 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210195 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210195 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210195 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210195 TableForm[cu]
%t A210195 Flatten[%]   (* A210195 *)
%t A210195 Table[Expand[v[n, x]], {n, 1, z}]
%t A210195 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210195 TableForm[cv]
%t A210195 Flatten[%]   (* A210196 *)
%Y A210195 Cf. A210196, A208510.
%K A210195 nonn,tabf
%O A210195 1,2
%A A210195 _Clark Kimberling_, Mar 18 2012