A210878 Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.

1, 0, 3, 0, 4, 7, 0, 2, 14, 17, 0, 2, 12, 46, 41, 0, 2, 8, 54, 140, 99, 0, 2, 8, 42, 212, 408, 239, 0, 2, 8, 34, 200, 758, 1154, 577, 0, 2, 8, 34, 160, 866, 2544, 3194, 1393, 0, 2, 8, 34, 144, 754, 3448, 8154, 8696, 3363, 0, 2, 8, 34, 144, 642, 3400, 12850

Offset

1,3

Comments

Leading coefficient of u(n,x): A001333

Limiting row: 0,2,8,34,144,610,...(Fibonacci numbers)

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

Links

Table of n, a(n) for n=1..63.

Formula

u(n,x)=x*u(n-1,x)+2x*v(n-1,x),

v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

Example

First six rows:
1
0...3
0...4...7
0...2...14...17
0...2...12...46...41
0...2...8....54...140...99
First three polynomials u(n,x): 1, 3x, 4x + 7x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A210878 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210879 *)

Crossrefs

Cf. A210879, A208510.

Sequence in context: A111493 A190181 A145092 * A355977 A356581 A367480

Adjacent sequences: A210875 A210876 A210877 * A210879 A210880 A210881

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 30 2012

Status

approved