A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section.

1, 2, 1, 2, 5, 1, 2, 6, 12, 1, 2, 6, 19, 27, 1, 2, 6, 20, 57, 58, 1, 2, 6, 20, 67, 160, 121, 1, 2, 6, 20, 68, 218, 424, 248, 1, 2, 6, 20, 68, 231, 680, 1073, 503, 1, 2, 6, 20, 68, 232, 775, 2028, 2619, 1014, 1, 2, 6, 20, 68, 232, 791, 2543, 5797, 6214, 2037, 1, 2

Offset: 1

Author

Clark Kimberling, Mar 19 2012

Keywords

• nonn
• tabl

Comments

Limiting row: A006012

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,...

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

Examples

			First five rows:
1
2...1
2...5...1
2...6...12...1
2...6...19...27...1
First three polynomials u(n,x): 1, 2 + x, 2 + 5x + x^2.
		

Crossrefs

Cf. A210218, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := x*u[n - 1, x] + 2 x*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[%]    (* A210217 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210218 *)

Formula

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

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

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