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A209689 Triangle of coefficients of polynomials u(n,x) jointly generated with A209690; see the Formula section. 3
1, 0, 2, 0, 2, 3, 0, 1, 6, 4, 0, 1, 4, 13, 5, 0, 1, 3, 13, 24, 6, 0, 1, 3, 9, 35, 40, 7, 0, 1, 3, 8, 28, 81, 62, 8, 0, 1, 3, 8, 22, 82, 167, 91, 9, 0, 1, 3, 8, 21, 64, 217, 315, 128, 10, 0, 1, 3, 8, 21, 56, 188, 519, 554, 174, 11, 0, 1, 3, 8, 21, 55, 155, 529, 1136, 921 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Combinatorial limit of rows:  even-indexed Fibonacci numbers. For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..76.

FORMULA

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

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

0...2

0...2...3

0...1...6...4

0...1...4...13...5

First three polynomials v(n,x): 1, 2x, 2x + 3x^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] + 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[%]    (* A209689 *)

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

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

TableForm[cv]

Flatten[%]   (* A209690 *)

CROSSREFS

Cf. A209690, A208510.

Sequence in context: A323474 A132814 A058623 * A204329 A111565 A299761

Adjacent sequences:  A209686 A209687 A209688 * A209690 A209691 A209692

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified July 20 22:54 EDT 2019. Contains 325189 sequences. (Running on oeis4.)