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A209564 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section. 3
1, 1, 2, 1, 2, 3, 1, 2, 5, 4, 1, 2, 5, 11, 5, 1, 2, 5, 13, 21, 6, 1, 2, 5, 13, 32, 36, 7, 1, 2, 5, 13, 34, 72, 57, 8, 1, 2, 5, 13, 34, 87, 148, 85, 9, 1, 2, 5, 13, 34, 89, 212, 281, 121, 10, 1, 2, 5, 13, 34, 89, 231, 485, 499, 166, 11, 1, 2, 5, 13, 34, 89, 233, 585, 1039 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A209563:  first k terms of row n are F(2), ..., F(2k), where F = A000045 (Fibonacci numbers) and k=floor ((n+1)/2).

A209564:  first k terms of row n are F(1), ..., F(2k-1), where k=floor ((n+2)/2).

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)+v(n-1,x),

v(n,x)=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

1...2

1...2...3

1...2...5...4

1...2...5...11...1

First three polynomials v(n,x): 1, 1+2x , 1+2x+3x^2 .

MATHEMATICA

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

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

v[n_, x_] := 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[%]   (* A209563 *)

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

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

TableForm[cv]

Flatten[%]   (* A209564 *)

CROSSREFS

Cf. A209563, A208510.

Sequence in context: A064882 A065158 A181842 * A029653 A067763 A263683

Adjacent sequences:  A209561 A209562 A209563 * A209565 A209566 A209567

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)