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A210603 Triangle of coefficients of polynomials u(n,x) jointly generated with A210738; see the Formula section. 3
1, 2, 2, 4, 6, 4, 7, 17, 16, 8, 12, 39, 57, 40, 16, 20, 84, 159, 169, 96, 32, 33, 170, 405, 551, 465, 224, 64, 54, 332, 950, 1608, 1727, 1217, 512, 128, 88, 630, 2115, 4264, 5655, 5055, 3073, 1152, 256, 143, 1171, 4515, 10603, 16666, 18294, 14079 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with F(n+2)-1, where F=A000045 (Fibonacci

numbers), and ends with 2^(n-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)=2x*u(n-1,x)+v(n-1,x)+1,

v(n,x)=(x+1)*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....4

7....17...16...8

12...39...57...40...16

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

MATHEMATICA

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

u[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;

v[n_, x_] := (x + 1)*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[%]    (* A210603 *)

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

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

TableForm[cv]

Flatten[%]    (* A210738 *)

CROSSREFS

Cf. A210738, A208510.

Sequence in context: A085730 A232065 A219741 * A252820 A218765 A219310

Adjacent sequences:  A210600 A210601 A210602 * A210604 A210605 A210606

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified November 22 05:52 EST 2018. Contains 317453 sequences. (Running on oeis4.)