A210750 - OEIS

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

%S 1,2,3,4,8,7,7,21,24,15,12,46,78,64,31,20,96,205,247,160,63,33,190,

%T 501,756,712,384,127,54,365,1140,2109,2483,1929,896,255,88,684,2480,

%U 5404,7764,7538,5002,2048,511,143,1259,5199,13083,22070,26058

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section.

%C Row n starts with -1+F(n+2) and ends with -1+2^n, where F=A000045 (Fibonacci numbers).

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

%F u(n,x)=(x+1)*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 2....3

%e 4....8....7

%e 7....21...24...15

%e 12...46...78...64...31

%e First three polynomials v(n,x): 1, 2 + 3x, 4 + 8x +7x^2

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

%t u[n_, x_] := (x + 1)*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[%]    (* A210749 *)

%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[%]    (* A210750 *)

%Y Cf. A210749, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 25 2012