A210230 Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.

1, 3, 1, 6, 4, 1, 11, 11, 5, 1, 19, 26, 17, 6, 1, 32, 56, 48, 24, 7, 1, 53, 114, 121, 78, 32, 8, 1, 87, 223, 283, 223, 117, 41, 9, 1, 142, 424, 627, 584, 372, 166, 51, 10, 1, 231, 789, 1334, 1434, 1073, 579, 226, 62, 11, 1, 375, 1444, 2750, 3352, 2879, 1818

Offset

1,2

Comments

Alternating row sums: 1,2,3,4,5,6,... (A000027)

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

Links

Table of n, a(n) for n=1..61.

Formula

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

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

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

Example

First five rows:
1
3....1
6....4....1
11...11...5....1
19...26...17...6...1
First three polynomials v(n,x): 1, 3 + x , 6 + 4x + x^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] + 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[%]     (* A210229 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210230 *)

Crossrefs

Cf. A210229, A208510.

Sequence in context: A108286 A185944 A131415 * A207615 A209165 A121437

Adjacent sequences: A210227 A210228 A210229 * A210231 A210232 A210233

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved