A209759 Triangle of coefficients of polynomials u(n,x) jointly generated with A209760; see the Formula section.

1, 1, 2, 1, 5, 5, 1, 5, 16, 13, 1, 5, 19, 48, 34, 1, 5, 19, 68, 141, 89, 1, 5, 19, 71, 233, 409, 233, 1, 5, 19, 71, 262, 772, 1175, 610, 1, 5, 19, 71, 265, 948, 2492, 3349, 1597, 1, 5, 19, 71, 265, 986, 3354, 7879, 9482, 4181, 1, 5, 19, 71, 265, 989, 3641

Offset

1,3

Comments

Limiting row: A001834

Coefficient of x^n in u(n,x): odd-indexed Fibonacci numbers

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...; A033999

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

Links

Table of n, a(n) for n=1..62.

Formula

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

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

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

Example

First five rows:
1
1...2
1...5...5
1...5...16...13
1...5...19...48...34
First three polynomials u(n,x): 1, 1 + 2x, 1 + 5x + 5x^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*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[%]    (* A209759 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209760 *)

Crossrefs

Cf. A209760, A208510.

Sequence in context: A300661 A145882 A209765 * A111785 A304462 A021468

Adjacent sequences: A209756 A209757 A209758 * A209760 A209761 A209762

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved