A210796 Triangle of coefficients of polynomials v(n,x) jointly generated with A210795; see the Formula section.

1, 1, 2, 3, 3, 3, 3, 7, 6, 5, 5, 10, 16, 12, 8, 5, 16, 26, 34, 23, 13, 7, 21, 47, 64, 70, 43, 21, 7, 29, 68, 123, 147, 140, 79, 34, 9, 36, 104, 200, 304, 324, 274, 143, 55, 9, 46, 140, 324, 538, 714, 690, 527, 256, 89, 11, 55, 195, 480, 932, 1366, 1616, 1431

Offset

1,3

Comments

Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Column 2: A114113

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

Links

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

Formula

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

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

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

Example

First five rows:
1
1...2
3...3....3
3...7....6....5
5...10...16...12...8
First three polynomials v(n,x): 1, 1 + 2x, 3 + 3x + 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 = 1; h = 2; p = -1; f = 0;
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[%]   (* A210795 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210796 *)

Crossrefs

Cf. A210795, A208510.

Sequence in context: A200924 A111913 A354142 * A305419 A075757 A096420

Adjacent sequences: A210793 A210794 A210795 * A210797 A210798 A210799

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 26 2012

Status

approved