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

1, 2, 2, 4, 4, 4, 7, 10, 8, 8, 12, 20, 24, 16, 16, 20, 40, 52, 56, 32, 32, 33, 76, 116, 128, 128, 64, 64, 54, 142, 240, 312, 304, 288, 128, 128, 88, 260, 488, 688, 800, 704, 640, 256, 256, 143, 470, 964, 1496, 1856, 1984, 1600, 1408, 512, 512, 232, 840

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Formula

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

v(n,x)=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
4....4....4
7....10...8....8
12...20...24...16...16
First three polynomials v(n,x): 1, 2 + 2x , 4 + 4x + 4x^2.

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. A210035, A208510.

Sequence in context: A367039 A115383 A219156 * A304230 A305586 A305040

Adjacent sequences: A210033 A210034 A210035 * A210037 A210038 A210039

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 16 2012

Status

approved