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A209168 Triangle of coefficients of polynomials u(n,x) jointly generated with A209169; see the Formula section. 3
1, 2, 1, 4, 6, 3, 7, 16, 17, 7, 12, 37, 56, 47, 17, 20, 78, 154, 182, 128, 41, 33, 156, 378, 574, 565, 344, 99, 54, 301, 864, 1590, 1995, 1697, 915, 239, 88, 566, 1877, 4048, 6118, 6605, 4973, 2413, 577, 143, 1044, 3927, 9693, 17073, 22128, 21093 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n begins with F(n+2)-1, 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..52.

FORMULA

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

v(n,x)=(x+1)*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....1

4....6....3

7....16...17...7

12...37...56...47...17

First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^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] + 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[%]    (* A209168 *)

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

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

TableForm[cv]

Flatten[%]    (* A209169 *)

CROSSREFS

Cf. A209169, A208510.

Sequence in context: A105364 A180405 A171007 * A209162 A127366 A064786

Adjacent sequences:  A209165 A209166 A209167 * A209169 A209170 A209171

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 08 2012

STATUS

approved

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Last modified October 19 10:58 EDT 2019. Contains 328216 sequences. (Running on oeis4.)