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

1, 2, 1, 4, 4, 1, 7, 12, 7, 1, 12, 29, 28, 11, 1, 20, 64, 86, 56, 16, 1, 33, 132, 230, 210, 101, 22, 1, 54, 261, 560, 662, 451, 169, 29, 1, 88, 500, 1279, 1860, 1646, 883, 267, 37, 1, 143, 936, 2785, 4819, 5257, 3682, 1611, 403, 46, 1, 232, 1721, 5848

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..58.

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
2....1
4....4....1
7....12...7....1
12...29...28...11...1
First three polynomials u(n,x): 1, 2 + x, 4 + 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] + (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. A210236, A208510.

Sequence in context: A333650 A214984 A118976 * A138177 A101559 A220537

Adjacent sequences: A210232 A210233 A210234 * A210236 A210237 A210238

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved