A209143 Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.

1, 2, 1, 5, 4, 11, 11, 1, 23, 28, 6, 47, 68, 23, 1, 95, 160, 74, 8, 191, 368, 216, 39, 1, 383, 832, 592, 152, 10, 767, 1856, 1552, 520, 59, 1, 1535, 4096, 3936, 1632, 270, 12, 3071, 8960, 9728, 4816, 1060, 83, 1, 6143, 19456, 23552, 13568, 3752, 436

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..54.

Formula

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

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

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

Example

First five rows:
1
2....1
5....4
11...11...1
23...28...6
First three polynomials u(n,x):  1, 2 + x, 5 + 4x

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 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[%]    (* A209143 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209144 *)

Crossrefs

Cf. A209144, A208510.

Sequence in context: A091802 A144240 A233525 * A243274 A119914 A152192

Adjacent sequences: A209140 A209141 A209142 * A209144 A209145 A209146

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 06 2012

Status

approved