A210751 Triangle of coefficients of polynomials u(n,x) jointly generated with A210752; see the Formula section.

1, 2, 2, 3, 6, 5, 4, 12, 19, 13, 5, 20, 46, 59, 34, 6, 30, 90, 166, 179, 89, 7, 42, 155, 370, 572, 533, 233, 8, 56, 245, 715, 1426, 1904, 1564, 610, 9, 72, 364, 1253, 3046, 5240, 6171, 4536, 1597, 10, 90, 516, 2044, 5845, 12237, 18561, 19581, 13031

Offset

1,2

Comments

Row n starts with n and ends with F(2n-1), where F=A000045 (Fibonacci numbers).

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

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=(x+1)*u(n-1,x)+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...2
3...6....5
4...12...19...13
5...20...46...59...34
First three polynomials u(n,x): 1, 2 + 2x, 3 + 6x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + 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[%]    (* A210751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210752 *)

Crossrefs

Cf. A210752, A208510.

Sequence in context: A207623 A116447 A137757 * A279791 A328744 A345706

Adjacent sequences: A210748 A210749 A210750 * A210752 A210753 A210754

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved