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A210597 Triangle of coefficients of polynomials u(n,x) jointly generated with A210602; see the Formula section. 3
1, 2, 2, 4, 5, 4, 7, 13, 12, 8, 12, 28, 37, 28, 16, 20, 58, 92, 98, 64, 32, 33, 114, 217, 273, 248, 144, 64, 54, 218, 479, 713, 760, 608, 320, 128, 88, 407, 1018, 1727, 2161, 2024, 1456, 704, 256, 143, 747, 2093, 3997, 5662, 6194, 5216, 3424, 1536, 512 (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..55.

FORMULA

u(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

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

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

EXAMPLE

First five rows:

1

2....2

4....5....4

7....13...12...8

12...28...37...28...16

First three polynomials u(n,x): 1, 2+ 2x, 4 + 5x + 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] + 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[%]    (* A210597 *)

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

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

TableForm[cv]

Flatten[%]    (* A210602 *)

CROSSREFS

Cf. A210602, A208510.

Sequence in context: A202876 A128900 A136099 * A252836 A286101 A072454

Adjacent sequences:  A210594 A210595 A210596 * A210598 A210599 A210600

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 24 2012

STATUS

approved

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Last modified October 18 00:15 EDT 2019. Contains 328135 sequences. (Running on oeis4.)