A210213 Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section.

1, 2, 1, 4, 3, 1, 7, 9, 4, 1, 12, 21, 16, 5, 1, 20, 46, 46, 25, 6, 1, 33, 94, 121, 85, 36, 7, 1, 54, 185, 289, 260, 141, 49, 8, 1, 88, 353, 653, 708, 491, 217, 64, 9, 1, 143, 659, 1409, 1800, 1499, 847, 316, 81, 10, 1, 232, 1209, 2939, 4320, 4229, 2863, 1366

Offset: 1

Author

Clark Kimberling, Mar 19 2012

Keywords

• nonn
• tabl

Comments

Row sums: even-indexed Fibonacci numbers

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

Examples

			First five rows:
1
2....1
4....3....1
7....9....4....1
12...21...16...5...1
First three polynomials u(n,x): 1, 2 + x, 4 + 3x + x^2.
		

Crossrefs

Cf. A210214, 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_] := u[n - 1, x] + (x + 1)*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[%]    (* A210213 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210214 *)

Formula

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

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

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