A210555 Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.

1, 1, 2, 1, 3, 4, 1, 4, 7, 8, 1, 5, 10, 17, 16, 1, 6, 13, 28, 39, 32, 1, 7, 16, 41, 70, 89, 64, 1, 8, 19, 56, 109, 176, 199, 128, 1, 9, 22, 73, 156, 297, 426, 441, 256, 1, 10, 25, 92, 211, 456, 765, 1020, 967, 512, 1, 11, 28, 113, 274, 657, 1236, 1953, 2398

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..64.

Formula

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

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

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

Example

First five rows:
1
1...2
1...3...4
1...4...7....8
1...5...10...17...16
First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := x*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[%]   (* A208341 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210554 *)

Crossrefs

Cf. A210554, A208510.

Sequence in context: A132110 A039912 A163311 * A008949 A076832 A078925

Adjacent sequences: A210552 A210553 A210554 * A210556 A210557 A210558

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 22 2012

Status

approved