A210234 Triangle of coefficients of polynomials v(n,x) jointly generated with A210233; see the Formula section.

1, 2, 3, 3, 7, 7, 4, 14, 20, 15, 5, 22, 50, 53, 31, 6, 33, 92, 157, 134, 63, 7, 45, 161, 335, 455, 327, 127, 8, 60, 248, 666, 1112, 1248, 776, 255, 9, 76, 372, 1150, 2466, 3448, 3288, 1801, 511, 10, 95, 520, 1910, 4732, 8426, 10144, 8399, 4106, 1023, 11

Offset

1,2

Comments

First and last terms of row n: n and -1+2^n

Alternating row sums: 3^(n-1)

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

Links

Table of n, a(n) for n=1..56.

Formula

u(n,x)=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.

Example

First five rows:
1
2...3
3...7....7
4...14...20...15
5...22...50...53...31
First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^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_] := (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[%]      (* A210233 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]      (* A210234 *)

Crossrefs

Cf. A210233, A208510.

Sequence in context: A108346 A210558 A208920 * A209768 A209169 A222294

Adjacent sequences: A210231 A210232 A210233 * A210235 A210236 A210237

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved