A209692 - OEIS

A209692

Triangle of coefficients of polynomials v(n,x) jointly generated with A209691; see the Formula section.

1, 2, 2, 1, 6, 4, 1, 4, 16, 8, 1, 3, 16, 40, 16, 1, 3, 11, 56, 96, 32, 1, 3, 10, 43, 176, 224, 64, 1, 3, 10, 35, 163, 512, 512, 128, 1, 3, 10, 34, 128, 579, 1408, 1152, 256, 1, 3, 10, 34, 117, 477, 1923, 3712, 2560, 512, 1, 3, 10, 34

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OFFSET

1,2

COMMENTS

Combinatorial limit of rows: A007052.

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

LINKS

Table of n, a(n) for n=1..59.

FORMULA

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

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

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

EXAMPLE

First five rows:

2...2

1...6...4

1...4...16...8

1...3...16...40...16

First three polynomials v(n,x): 1, 2 + 2x , 1 + 6x + 4x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];

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[%] (* A209691 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%] (* A209692 *)

CROSSREFS

Cf. A209691, A208510.

Sequence in context: A220963 A375566 A179313 * A178886 A065052 A128308

Adjacent sequences: A209689 A209690 A209691 * A209693 A209694 A209695

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved