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A209167 Triangle of coefficients of polynomials v(n,x) jointly generated with A209166; see the Formula section. 3
1, 2, 2, 3, 5, 3, 5, 12, 12, 5, 8, 25, 35, 25, 8, 13, 50, 89, 89, 50, 13, 21, 96, 207, 263, 207, 96, 21, 34, 180, 455, 698, 698, 455, 180, 34, 55, 331, 959, 1719, 2073, 1719, 959, 331, 55, 89, 600, 1959, 4011, 5643, 5643, 4011, 1959, 600, 89, 144, 1075 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,1,0,...

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..57.

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

3....1

6....4....1

12...14...7....1

24...40...28...8...1

MATHEMATICA

First three polynomials v(n, x): 1, 3 + x, 6 + 4x + x^2.

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. A209166, A208510.

Sequence in context: A317043 A317697 A132403 * A299995 A113167 A036014

Adjacent sequences:  A209164 A209165 A209166 * A209168 A209169 A209170

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 08 2012

STATUS

approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)