A210232 Triangle of coefficients of polynomials v(n,x) jointly generated with A210231; see the Formula section.

1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 16, 25, 18, 5, 6, 24, 48, 54, 30, 6, 7, 33, 84, 123, 106, 47, 7, 8, 44, 132, 246, 282, 194, 70, 8, 9, 56, 198, 438, 637, 594, 336, 100, 9, 10, 70, 280, 730, 1272, 1504, 1170, 556, 138, 10, 11, 85, 385, 1140, 2337, 3337, 3301

Offset

1,2

Comments

First and last terms of row n are n.

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...

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

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

Example

First five rows:
1
2...2
3...5....3
4...10...10...4
5...16...25...16...5
First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 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*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[%]     (* A210231 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210232 *)

Crossrefs

Cf. A210231, A208510.

Sequence in context: A125101 A208519 A336725 * A047666 A285935 A209568

Adjacent sequences: A210229 A210230 A210231 * A210233 A210234 A210235

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved