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

1, 1, 3, 1, 3, 8, 1, 3, 11, 21, 1, 3, 11, 38, 55, 1, 3, 11, 41, 124, 144, 1, 3, 11, 41, 150, 389, 377, 1, 3, 11, 41, 153, 533, 1187, 987, 1, 3, 11, 41, 153, 568, 1838, 3549, 2584, 1, 3, 11, 41, 153, 571, 2084, 6168, 10447, 6765, 1, 3, 11, 41, 153, 571, 2128

Offset

1,3

Comments

Limiting row: A001835

Coefficient of x^n in v(n,x): even-indexed Fibonacci numbers

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...3
1...3...8
1...3...11...21
1...3...11...38...55
First three polynomials v(n,x): 1, 1 + 3x , 1 + 3x + 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*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. A208510.

Sequence in context: A328807 A103279 A208910 * A046544 A011088 A352794

Adjacent sequences: A209757 A209758 A209759 * A209761 A209762 A209763

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved