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A209147 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section. 3
1, 2, 2, 3, 5, 4, 5, 11, 12, 8, 8, 23, 33, 28, 16, 13, 45, 80, 90, 64, 32, 21, 86, 180, 245, 232, 144, 64, 34, 160, 387, 615, 696, 576, 320, 128, 55, 293, 801, 1454, 1913, 1880, 1392, 704, 256, 89, 529, 1614, 3284, 4902, 5586, 4896, 3296, 1536, 512, 144 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each row begins with a Fibonacci numbers and ends with a power of 2.  For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...2

3...5...4

5...11...12...8

8...23...33...28...16

First three polynomials v(n,x): 1, 2 + 2x, 3 + 5x + 4x^2.

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] + 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[%]    (* A209146 *)

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

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

TableForm[cv]

Flatten[%]    (* A209147 *)

CROSSREFS

Cf. A209146, A208510.

Sequence in context: A301964 A301884 A302081 * A327267 A036716 A026399

Adjacent sequences:  A209144 A209145 A209146 * A209148 A209149 A209150

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 06 2012

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)