A210222 Triangle of coefficients of polynomials v(n,x) jointly generated with A104698; see the Formula section.

1, 2, 2, 3, 6, 2, 4, 12, 10, 2, 5, 20, 28, 14, 2, 6, 30, 60, 52, 18, 2, 7, 42, 110, 140, 84, 22, 2, 8, 56, 182, 310, 276, 124, 26, 2, 9, 72, 280, 602, 726, 484, 172, 30, 2, 10, 90, 408, 1064, 1638, 1486, 780, 228, 34, 2, 11, 110, 570, 1752, 3304, 3850, 2750

Offset: 1

Author

Clark Kimberling, Mar 19 2012

Keywords

• nonn
• tabl

Comments

Period of alternating row sums: (1,0,-1,0)

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

Examples

			First five rows:
1
2...2
3...6....2
4...12...10...2
5...20...28...14...2
First three polynomials v(n,x): 1, 2 + 2x , 3 + 6x + 2x^2.
		

Crossrefs

Cf. A104698, 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_] := 2 x*u[n - 1, 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[%]     (* A104698 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210222 *)

Formula

u(n,x)=x*u(n-1,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.