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A210287 Triangle of coefficients of polynomials v(n,x) jointly generated with A209999; see the Formula section. 3
1, 3, 1, 6, 6, 1, 11, 18, 10, 1, 19, 45, 41, 15, 1, 32, 100, 130, 80, 21, 1, 53, 208, 352, 310, 141, 28, 1, 87, 413, 866, 994, 652, 231, 36, 1, 142, 794, 1991, 2828, 2429, 1253, 358, 45, 1, 231, 1490, 4358, 7391, 7871, 5348, 2248, 531, 55, 1, 375, 2745 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1: -2+F(n+3), where F=000045 (Fibonacci numbers)

Row sums: A003462

Alternating row sums: 1,2,1,2,1,2,1,2,1,2,1,2,1,2,...

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

3....1

6....6....1

11...18...10...1

19...45...41...15...1

First three polynomials v(n,x): 1, 3 + x , 6 + 6x + x^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. A209999, A208510.

Sequence in context: A325005 A325013 A152685 * A116412 A089511 A246257

Adjacent sequences:  A210284 A210285 A210286 * A210288 A210289 A210290

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 23 2012

STATUS

approved

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Last modified October 20 08:03 EDT 2019. Contains 328252 sequences. (Running on oeis4.)