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A210202 Triangle of coefficients of polynomials v(n,x) jointly generated with A210201; see the Formula section. 3
1, 2, 3, 4, 7, 6, 7, 17, 17, 12, 12, 35, 50, 40, 24, 20, 70, 120, 135, 92, 48, 33, 134, 275, 365, 346, 208, 96, 54, 251, 593, 930, 1033, 856, 464, 192, 88, 461, 1236, 2206, 2874, 2784, 2064, 1024, 384, 143, 835, 2500, 5015, 7389, 8355, 7240, 4880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: F(n+2)-1, where F=A000045 (Fibonacci numbers)

Row sums: A048473

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

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....3

4....7....6

7....17...17...12

12...35...50...40...24

First three polynomials v(n,x): 1, 2 + 3x , 4 + 7x + 6x^2.

MATHEMATICA

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

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

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[%]   (* A210201 *)

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

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

TableForm[cv]

Flatten[%]   (* A210202 *)

CROSSREFS

Cf. A210201, A208510.

Sequence in context: A120225 A247798 A130685 * A260436 A255553 A260742

Adjacent sequences:  A210199 A210200 A210201 * A210203 A210204 A210205

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 18 2012

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)