A209774 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.

1, 2, 3, 2, 7, 8, 3, 12, 25, 21, 3, 19, 56, 84, 55, 4, 26, 103, 227, 269, 144, 4, 36, 169, 486, 848, 833, 377, 5, 45, 259, 914, 2078, 2999, 2518, 987, 5, 58, 372, 1565, 4393, 8277, 10192, 7475, 2584, 6, 69, 518, 2503, 8342, 19420, 31269, 33600, 21881

Offset

1,2

Comments

Last term in row n: F(2n), where F=A000045, the 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*u(n-1,x)+(x+1)*v(n-1,x),

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...3
2...7....8
3...12...25...21
3...19...56...84...55
First three polynomials v(n,x): 1, 2 + 3x , 2 + 7x + 8x^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];
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[%]    (* A209773 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209774 *)

Crossrefs

Cf. A209673, A208510.

Sequence in context: A210564 A208930 A122076 * A271322 A373420 A170842

Adjacent sequences: A209771 A209772 A209773 * A209775 A209776 A209777

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved