A210603 Triangle of coefficients of polynomials u(n,x) jointly generated with A210738; see the Formula section.

1, 2, 2, 4, 6, 4, 7, 17, 16, 8, 12, 39, 57, 40, 16, 20, 84, 159, 169, 96, 32, 33, 170, 405, 551, 465, 224, 64, 54, 332, 950, 1608, 1727, 1217, 512, 128, 88, 630, 2115, 4264, 5655, 5055, 3073, 1152, 256, 143, 1171, 4515, 10603, 16666, 18294, 14079

Offset

1,2

Comments

Row n starts with F(n+2)-1, where F=A000045 (Fibonacci

numbers), and ends with 2^(n-1). For a discussion and

guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..52.

Formula

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

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

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

Example

First five rows:
1
2....2
4....6....4
7....17...16...8
12...39...57...40...16
First three polynomials u(n,x): 1, 2+ 2x, 4 + 6x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%]    (* A210603 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210738 *)

Crossrefs

Cf. A210738, A208510.

Sequence in context: A085730 A232065 A219741 * A252820 A218765 A219310

Adjacent sequences: A210600 A210601 A210602 * A210604 A210605 A210606

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved