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A210738 Triangle of coefficients of polynomials v(n,x) jointly generated with A210603; see the Formula section. 3
1, 3, 2, 6, 9, 4, 11, 25, 23, 8, 19, 60, 81, 55, 16, 32, 130, 237, 233, 127, 32, 53, 266, 610, 798, 625, 287, 64, 87, 522, 1451, 2364, 2439, 1601, 639, 128, 142, 995, 3255, 6373, 8138, 6984, 3969, 1407, 256, 231, 1855, 6995, 16007, 24430, 25832 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n starts with F(n+3)-2, 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..51.

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

3....2

6....9....4

11...25...23...8

19...60...81...55...16

First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x + 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. A210603, A208510.

Sequence in context: A072635 A318049 A210754 * A210601 A197493 A300070

Adjacent sequences:  A210735 A210736 A210737 * A210739 A210740 A210741

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 14 04:44 EDT 2019. Contains 327995 sequences. (Running on oeis4.)