A210550 Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.

1, 2, 2, 2, 6, 4, 2, 7, 16, 8, 2, 7, 23, 40, 16, 2, 7, 24, 71, 96, 32, 2, 7, 24, 81, 207, 224, 64, 2, 7, 24, 82, 266, 575, 512, 128, 2, 7, 24, 82, 279, 843, 1535, 1152, 256, 2, 7, 24, 82, 280, 939, 2572, 3967, 2560, 512, 2, 7, 24, 82, 280, 955, 3102, 7565, 9983

Offset: 1

Author

Clark Kimberling, Mar 22 2012

Keywords

• nonn
• tabl

Comments

Row sums: -1+odd-indexed Fibonacci numbers

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

Examples

			First five rows:
2
2...2
2...6...4
2...7...16....8
2...7...28....40...16
First three polynomials v(n,x): 2, 2 + 2x , 2 + 6x + 4x^2.
		

Crossrefs

Cf. A210549, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, 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[%]    (* A210549 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210550 *)

Formula

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

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

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