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A210806 Triangle of coefficients of polynomials v(n,x) jointly generated with A210805; see the Formula section. 4
1, 0, 2, 1, 1, 3, 0, 3, 3, 5, 1, 2, 8, 7, 8, 0, 4, 8, 19, 15, 13, 1, 3, 15, 25, 42, 30, 21, 0, 5, 15, 46, 67, 89, 58, 34, 1, 4, 24, 58, 128, 164, 182, 109, 55, 0, 6, 24, 90, 186, 330, 378, 363, 201, 89, 1, 5, 35, 110, 300, 536, 804, 833, 709, 365, 144, 0, 7, 35, 155 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row n ends with F(n), where F=A000045 (Fibonacci numbers).

Column 1:  1,0,1,0,1,0,1,0,...

Alternating row sums:  signed Fibonacci numbers.

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

LINKS

Table of n, a(n) for n=1..70.

FORMULA

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

v(n,x)=(x+2)*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

0...2

1...1...3

0...3...3...5

1...2...8...7...8

First three polynomials v(n,x): 1, 2x, 1 + x + 3x^2

MATHEMATICA

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

u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;

d[x_] := h + x; e[x_] := p + x;

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

j = 0; c = 0; h = 2; p = -1; f = -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[%]   (* A210805 *)

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

TableForm[cv]

Flatten[%]   (* A210806 *)

CROSSREFS

Cf. A210805, A208510.

Sequence in context: A033804 A103910 A155993 * A147867 A227431 A114118

Adjacent sequences:  A210803 A210804 A210805 * A210807 A210808 A210809

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 27 2012

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)