cp's OEIS Frontend

A210035 Triangle of coefficients of polynomials u(n,x) jointly generated with A210036; see the Formula section.

%I A210035 #4 Mar 30 2012 18:58:16
%S A210035 1,3,6,2,11,6,4,19,16,12,8,32,36,36,24,16,53,76,88,80,48,32,87,152,
%T A210035 204,208,176,96,64,142,294,444,520,480,384,192,128,231,554,932,1208,
%U A210035 1280,1088,832,384,256,375,1024,1896,2704,3136,3072,2432,1792,768
%N A210035 Triangle of coefficients of polynomials u(n,x) jointly generated with A210036; see the Formula section.
%C A210035 For a discussion and guide to related arrays, see A208510.
%F A210035 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210035 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A210035 where u(1,x)=1, v(1,x)=1.
%e A210035 First five rows:
%e A210035 1
%e A210035 3
%e A210035 6....2
%e A210035 11...6....4
%e A210035 19...16...12...8
%e A210035 First three polynomials u(n,x): 1, 3, 6 + 2x.
%t A210035 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210035 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210035 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210035 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210035 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210035 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210035 TableForm[cu]
%t A210035 Flatten[%]    (* A210035 *)
%t A210035 Table[Expand[v[n, x]], {n, 1, z}]
%t A210035 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210035 TableForm[cv]
%t A210035 Flatten[%]    (* A210036 *)
%Y A210035 Cf. A210036, A208510.
%K A210035 nonn,tabl
%O A210035 1,2
%A A210035 _Clark Kimberling_, Mar 16 2012