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A209166 Triangle of coefficients of polynomials u(n,x) jointly generated with A209167; see the Formula section. 3
1, 2, 1, 4, 5, 2, 7, 13, 10, 3, 12, 30, 34, 20, 5, 20, 63, 94, 80, 38, 8, 33, 126, 233, 258, 177, 71, 13, 54, 243, 536, 728, 647, 374, 130, 21, 88, 457, 1171, 1881, 2043, 1527, 765, 235, 34, 143, 843, 2461, 4559, 5835, 5319, 3443, 1525, 420, 55, 232 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n begins with F(n+2)-1 and ends with F(n), where F=A000045 (Fibonacci numbers).

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

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

EXAMPLE

First five rows:

1

2....1

5....5....1

11...15...6....1

23...41...27...9...1

First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^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_] := (x + 1)*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[%]    (* A209166 *)

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

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

TableForm[cv]

Flatten[%]    (* A209167 *)

CROSSREFS

Cf. A209167, A208510.

Sequence in context: A214736 A051176 A145064 * A209146 A209154 A144332

Adjacent sequences:  A209163 A209164 A209165 * A209167 A209168 A209169

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 08 2012

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)