A210035 Triangle of coefficients of polynomials u(n,x) jointly generated with A210036; see the Formula section.

1, 3, 6, 2, 11, 6, 4, 19, 16, 12, 8, 32, 36, 36, 24, 16, 53, 76, 88, 80, 48, 32, 87, 152, 204, 208, 176, 96, 64, 142, 294, 444, 520, 480, 384, 192, 128, 231, 554, 932, 1208, 1280, 1088, 832, 384, 256, 375, 1024, 1896, 2704, 3136, 3072, 2432, 1792, 768

Offset

1,2

Comments

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

Links

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

Formula

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

v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,

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

Example

First five rows:
1
3
6....2
11...6....4
19...16...12...8
First three polynomials u(n,x): 1, 3, 6 + 2x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 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[%]    (* A210035 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210036 *)

Crossrefs

Cf. A210036, A208510.

Sequence in context: A364365 A210189 A257506 * A210199 A268717 A002516

Adjacent sequences: A210032 A210033 A210034 * A210036 A210037 A210038

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 16 2012

Status

approved