cp's OEIS Frontend

A210742 Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section.

%I A210742 #5 Mar 30 2012 18:58:17
%S A210742 1,3,2,5,9,5,7,20,27,13,9,35,73,80,34,11,54,151,252,234,89,13,77,269,
%T A210742 597,837,677,233,15,104,435,1199,2225,2702,1941,610,17,135,657,2158,
%U A210742 4956,7943,8533,5523,1597,19,170,943,3590,9796,19387,27435,26479
%N A210742 Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section.
%C A210742 Row n starts with 2n-1 and ends with an odd-indexed
%C A210742 Fibonacci number.
%C A210742 Row sums: A035344
%C A210742 Alternate row sums: 1,1,1,1,1,1,1,1,...
%C A210742 For a discussion and guide to related arrays, see A208510.
%F A210742 u(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A210742 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210742 where u(1,x)=1, v(1,x)=1.
%e A210742 First five rows:
%e A210742 1
%e A210742 3...2
%e A210742 5...9....5
%e A210742 7...20...27...13
%e A210742 9...35...73...80...34
%e A210742 First three polynomials v(n,x): 1, 3 + 2x, 5 + 9x + 5x^2
%t A210742 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210742 u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210742 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210742 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210742 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210742 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210742 TableForm[cu]
%t A210742 Flatten[%]     (* A210741 *)
%t A210742 Table[Expand[v[n, x]], {n, 1, z}]
%t A210742 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210742 TableForm[cv]
%t A210742 Flatten[%]     (* A210742 *)
%Y A210742 Cf. A210741, A208510.
%K A210742 nonn,tabl
%O A210742 1,2
%A A210742 _Clark Kimberling_, Mar 24 2012