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A209999 Triangle of coefficients of polynomials u(n,x) jointly generated with A210287; see the Formula section. 4
1, 2, 2, 4, 6, 3, 7, 16, 13, 4, 12, 36, 44, 24, 5, 20, 76, 122, 100, 40, 6, 33, 152, 306, 332, 201, 62, 7, 54, 294, 712, 968, 783, 370, 91, 8, 88, 554, 1573, 2572, 2614, 1666, 637, 128, 9, 143, 1024, 3339, 6392, 7829, 6296, 3277, 1040, 174, 10, 232, 1864 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: -1+F(n+2), where F=000045 (Fibonacci numbers)

Row sums: A003462

Alternating row sums: 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)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,

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

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

EXAMPLE

First five rows:

1

2....2

4....6....3

7....16...13...4

12...36...44...24...5

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

MATHEMATICA

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

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

v[n_, x_] := u[n - 1, x] + (x + 1)*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[%]    (* A209999 *)

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

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

TableForm[cv]

Flatten[%]    (* A210287 *)

CROSSREFS

Cf. A210287, A208510.

Sequence in context: A286243 A305125 A260095 * A127718 A115068 A051495

Adjacent sequences:  A209996 A209997 A209998 * A210000 A210001 A210002

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 23 2012

STATUS

approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)