A210600 Triangle of coefficients of polynomials u(n,x) jointly generated with A210601; see the Formula section.

1, 2, 2, 4, 7, 4, 7, 19, 20, 8, 12, 44, 69, 52, 16, 20, 94, 196, 218, 128, 32, 33, 190, 497, 731, 632, 304, 64, 54, 370, 1167, 2139, 2440, 1728, 704, 128, 88, 701, 2594, 5701, 8081, 7544, 4528, 1600, 256, 143, 1301, 5533, 14195, 24062, 27874, 22048

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..52.

Formula

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

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

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

Example

First five rows:
1
2....2
4....7....4
7....19...20...8
12...44...69...52...16
First three polynomials u(n,x): 1, 2+ 2x, 4 + 7x + 4x^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] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*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[%]    (* A210600 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210601 *)

Crossrefs

Cf. A210601, A208510.

Sequence in context: A209142 A368518 A115754 * A220308 A203975 A270246

Adjacent sequences: A210597 A210598 A210599 * A210601 A210602 A210603

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 24 2012

Status

approved