A210236 Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section.

1, 3, 2, 6, 8, 3, 11, 22, 16, 4, 19, 52, 57, 28, 5, 32, 112, 166, 124, 45, 6, 53, 228, 428, 432, 241, 68, 7, 87, 446, 1018, 1300, 984, 432, 98, 8, 142, 848, 2285, 3540, 3397, 2036, 728, 136, 9, 231, 1578, 4912, 8964, 10443, 7962, 3914, 1168, 183, 10

Offset

1,2

Comments

Row sums: powers of 3

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

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

Links

Table of n, a(n) for n=1..55.

Formula

u(n,x)=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.

Example

First five rows:
1
3....2
6....8....3
11...22...16...4
19...52...57...28...5
First three polynomials v(n,x): 1, 3 + 2x , 6 + 8x + 3x^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] + (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[%]      (* A210235 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]      (* A210236 *)

Crossrefs

Cf. A210235, A208510.

Sequence in context: A273344 A370665 A127717 * A193998 A209171 A368150

Adjacent sequences: A210233 A210234 A210235 * A210237 A210238 A210239

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved