A210879 Triangle of coefficients of polynomials v(n,x) jointly generated with A210878; see the Formula section.

1, 2, 2, 1, 5, 5, 1, 5, 16, 12, 1, 3, 21, 47, 29, 1, 3, 17, 79, 134, 70, 1, 3, 13, 79, 273, 373, 169, 1, 3, 13, 63, 333, 893, 1020, 408, 1, 3, 13, 55, 297, 1291, 2805, 2751, 985, 1, 3, 13, 55, 249, 1323, 4701, 8543, 7338, 2378, 1, 3, 13, 55, 233, 1147, 5525

Offset

1,2

Comments

Leading coefficient of v(n,x): A000129

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

Limiting row: 1,3,13,55,233,987...( 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)+2x*v(n-1,x),

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 six rows:
1
2...2
1...5...5
1...5...16...12
1...3...21...47....29
1...3...17...79...134...70
First three polynomials v(n,x): 1, 2 + 2x, 1 + 5x + 5x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x];
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[%]    (* A210878 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210879 *)

Crossrefs

Cf. A210878, A208510.

Sequence in context: A079218 A079220 A158068 * A176265 A187307 A280785

Adjacent sequences: A210876 A210877 A210878 * A210880 A210881 A210882

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 30 2012

Status

approved