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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..62.

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.

Example

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.

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 *)

Crossrefs

Cf. A104698, A208510.

Sequence in context: A083506 A248164 A338993 * A207621 A209157 A284785

Adjacent sequences: A210219 A210220 A210221 * A210223 A210224 A210225

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 19 2012

Status

approved