A210555 Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.

1, 1, 2, 1, 3, 4, 1, 4, 7, 8, 1, 5, 10, 17, 16, 1, 6, 13, 28, 39, 32, 1, 7, 16, 41, 70, 89, 64, 1, 8, 19, 56, 109, 176, 199, 128, 1, 9, 22, 73, 156, 297, 426, 441, 256, 1, 10, 25, 92, 211, 456, 765, 1020, 967, 512, 1, 11, 28, 113, 274, 657, 1236, 1953, 2398

Offset: 1

Author

Clark Kimberling, Mar 22 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			First five rows:
1
1...2
1...3...4
1...4...7....8
1...5...10...17...16
First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.
		

Crossrefs

Cf. A210554, 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_] := 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[%]   (* A208341 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210554 *)

Formula

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

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

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