A209820 Triangle of coefficients of polynomials v(n,x) jointly generated with A209819; see the Formula section.

1, 2, 2, 2, 6, 5, 2, 8, 18, 12, 2, 8, 30, 52, 29, 2, 8, 34, 104, 146, 70, 2, 8, 34, 136, 342, 402, 169, 2, 8, 34, 144, 514, 1080, 1090, 408, 2, 8, 34, 144, 594, 1848, 3306, 2920, 985, 2, 8, 34, 144, 610, 2360, 6370, 9872, 7746, 2378, 2, 8, 34, 144, 610, 2552

Offset

1,2

Comments

Let T(n,k) be the general term.

T(n,n): A000129

T(n,n-1): 2*A071667

Row sums: A003462

Alternating row sums: 1,0,1,0,1,0,1,0,...

Limiting row: F(3), F(6),F(9),...where F=A000045 (Fibonacci numbers)

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

Links

Table of n, a(n) for n=1..61.

Formula

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

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

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

Example

First five rows:
1
2...2
2...6...5
2...8...18...12
2...8...30...52...29
First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A209819 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209820 *)

Crossrefs

Cf. A209819, A208510.

Sequence in context: A309078 A241543 A210740 * A145890 A097091 A094204

Adjacent sequences: A209817 A209818 A209819 * A209821 A209822 A209823

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 23 2012

Status

approved