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A210805 Triangle of coefficients of polynomials u(n,x) jointly generated with A210806; see the Formula section. 3
1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 2, 6, 6, 5, 1, 3, 8, 14, 12, 8, 1, 3, 12, 22, 31, 23, 13, 1, 4, 15, 37, 56, 65, 43, 21, 1, 4, 20, 52, 102, 132, 132, 79, 34, 1, 5, 24, 76, 160, 260, 296, 261, 143, 55, 1, 5, 30, 100, 250, 446, 626, 639, 506, 256, 89, 1, 6, 35, 135, 360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).

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

LINKS

Table of n, a(n) for n=1..71.

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

1...1

1...1...2

1...2...3...3

1...2...6...6...5

First three polynomials u(n,x): 1, 1 + x, 1 + x + 2x^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. A210806, A208510.

Sequence in context: A100002 A227909 A301984 * A303842 A057041 A267177

Adjacent sequences:  A210802 A210803 A210804 * A210806 A210807 A210808

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 27 2012

STATUS

approved

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Last modified October 16 05:35 EDT 2019. Contains 328044 sequences. (Running on oeis4.)