A210201 Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section.

1, 3, 6, 3, 11, 10, 6, 19, 27, 23, 12, 32, 62, 73, 52, 24, 53, 132, 193, 187, 116, 48, 87, 266, 468, 552, 462, 256, 96, 142, 517, 1061, 1482, 1495, 1112, 560, 192, 231, 978, 2297, 3688, 4369, 3896, 2624, 1216, 384, 375, 1813, 4797, 8703, 11758

Offset: 1

Author

Clark Kimberling, Mar 18 2012

Keywords

• nonn
• tabf

Comments

Row sums: 3^(n-1)

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

Examples

			First five rows:
1
3
6....3
11...10...6
19...27...23...12
First three polynomials u(n,x): 1, 3, 6 + 3x.
		

Crossrefs

Cf. A210202, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]   (* A210201 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210202 *)

Formula

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

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

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