A210742 - OEIS

%I #5 Mar 30 2012 18:58:17

%S 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 597,837,677,233,15,104,435,1199,2225,2702,1941,610,17,135,657,2158,

%U 4956,7943,8533,5523,1597,19,170,943,3590,9796,19387,27435,26479

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

%C Row n starts with 2n-1 and ends with an odd-indexed

%C Fibonacci number.

%C Row sums: A035344

%C Alternate row sums: 1,1,1,1,1,1,1,1,...

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=2x*u(n-1,x)+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 5...9....5

%e 7...20...27...13

%e 9...35...73...80...34

%e First three polynomials v(n,x): 1, 3 + 2x, 5 + 9x + 5x^2

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := 2 x*u[n - 1, x] + 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[%]     (* A210741 *)

%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[%]     (* A210742 *)

%Y Cf. A210741, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 24 2012