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

1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 2, 6, 6, 5, 1, 3, 8, 14, 12, 8, 1, 3, 12, 22, 31, 23, 13, 1, 4, 15, 37, 56, 65, 43, 21, 1, 4, 20, 52, 102, 132, 132, 79, 34, 1, 5, 24, 76, 160, 260, 296, 261, 143, 55, 1, 5, 30, 100, 250, 446, 626, 639, 506, 256, 89, 1, 6, 35, 135, 360

Offset

1,6

Comments

Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).

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

Links

Table of n, a(n) for n=1..71.

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
1...1
1...1...2
1...2...3...3
1...2...6...6...5
First three polynomials u(n,x): 1, 1 + x, 1 + x + 2x^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. A210806, A208510.

Sequence in context: A328471 A227909 A301984 * A303842 A057041 A267177

Adjacent sequences: A210802 A210803 A210804 * A210806 A210807 A210808

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 27 2012

Status

approved