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

1, 2, 1, 3, 2, 2, 4, 5, 5, 3, 5, 8, 12, 9, 5, 6, 13, 22, 25, 17, 8, 7, 18, 38, 51, 51, 31, 13, 8, 25, 59, 98, 115, 101, 56, 21, 9, 32, 88, 166, 238, 248, 196, 100, 34, 10, 41, 124, 270, 438, 552, 520, 374, 177, 55, 11, 50, 170, 410, 762, 1090, 1234, 1064, 704

Offset: 1

Author

Clark Kimberling, Mar 26 2012

Keywords

• nonn
• tabl

Comments

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

Column 2: A000982

Column 3: A026035

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

Examples

			First five rows:
1
2...1
3...2...2
4...5...5....3
5...8...12...9...5
First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 2x^2.
		

Crossrefs

Cf. A210796, A208510.

Programs

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 *)

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.