A210203 Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section.

1, 3, 7, 2, 15, 10, 2, 31, 34, 14, 2, 63, 98, 62, 18, 2, 127, 258, 222, 98, 22, 2, 255, 642, 702, 418, 142, 26, 2, 511, 1538, 2046, 1538, 702, 194, 30, 2, 1023, 3586, 5630, 5122, 2942, 1090, 254, 34, 2, 2047, 8194, 14846, 15874, 11006, 5122, 1598, 322

Offset: 1

Author

Clark Kimberling, Mar 18 2012

Keywords

• nonn
• tabf

Comments

Column 1: -1+2^n

Row sums: 3^(n-1)

Alternating row sums: 1,1,1,1,1,1,1,1,1,...

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

Examples

			First five rows:
1
3
7....2
15...10...2
31...34...14...2
First three polynomials u(n,x): 1, 3, 7 + 2x.
		

Crossrefs

Cf. A210204, 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]+(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[%]   (* A210203 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210204 *)

Formula

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

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

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