A210806 Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section.

1, 0, 2, 1, 1, 3, 0, 3, 3, 5, 1, 2, 8, 7, 8, 0, 4, 8, 19, 15, 13, 1, 3, 15, 25, 42, 30, 21, 0, 5, 15, 46, 67, 89, 58, 34, 1, 4, 24, 58, 128, 164, 182, 109, 55, 0, 6, 24, 90, 186, 330, 378, 363, 201, 89, 1, 5, 35, 110, 300, 536, 804, 833, 709, 365, 144, 0, 7, 35, 155

Offset

1,3

Comments

Row n ends with F(n), where F=A000045 (Fibonacci numbers).

Column 1: 1,0,1,0,1,0,1,0,...

Alternating row sums: signed Fibonacci numbers.

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

Links

Table of n, a(n) for n=1..70.

Formula

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

v(n,x)=(x+2)*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
0...2
1...1...3
0...3...3...5
1...2...8...7...8
First three polynomials v(n,x): 1, 2x, 1 + x + 3x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 0; h = 2; p = -1; f = -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[%]   (* A210805 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210806 *)

Crossrefs

Cf. A210805, A208510.

Sequence in context: A155993 A353630 A341091 * A147867 A227431 A114118

Adjacent sequences: A210803 A210804 A210805 * A210807 A210808 A210809

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 27 2012

Status

approved