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A209690 Triangle of coefficients of polynomials v(n,x) jointly generated with A209689; see the Formula section. 4
1, 2, 1, 1, 4, 1, 1, 3, 7, 1, 1, 2, 9, 11, 1, 1, 2, 6, 22, 16, 1, 1, 2, 5, 19, 46, 22, 1, 1, 2, 5, 14, 54, 86, 29, 1, 1, 2, 5, 13, 42, 135, 148, 37, 1, 1, 2, 5, 13, 35, 124, 302, 239, 46, 1, 1, 2, 5, 13, 34, 99, 341, 617, 367, 56, 1, 1, 2, 5, 13, 34, 90, 287, 860, 1171 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..75.

FORMULA

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

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,

EXAMPLE

First five rows:

1

2...1

1...4...1

1...3...7...1

1...2...9...11...1

First three polynomials v(n,x): 1, 2 + x , 1 + 4x + x^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. A209689, A208510.

Sequence in context: A099238 A306846 A141450 * A061462 A294334 A122578

Adjacent sequences:  A209687 A209688 A209689 * A209691 A209692 A209693

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 12 2012

STATUS

approved

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Last modified May 22 21:17 EDT 2019. Contains 323504 sequences. (Running on oeis4.)