A210195 Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.

1, 3, 5, 4, 7, 12, 8, 9, 24, 32, 16, 11, 40, 80, 80, 32, 13, 60, 160, 240, 192, 64, 15, 84, 280, 560, 672, 448, 128, 17, 112, 448, 1120, 1792, 1792, 1024, 256, 19, 144, 672, 2016, 4032, 5376, 4608, 2304, 512, 21, 180, 960, 3360, 8064, 13440, 15360

Offset

1,2

Comments

Row sums: powers of 3

Periodic alternating row sums: 1,3,1,3,1,3,1,3,...

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

Links

Table of n, a(n) for n=1..53.

Formula

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

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

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

Example

First five rows:
1
3
5...4
7...12...8
9...24...32...16
First three polynomials u(n,x): 1, 3, 5 + 4x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 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[%]   (* A210195 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210196 *)

Crossrefs

Cf. A210196, A208510.

Sequence in context: A277897 A082568 A242640 * A069918 A361709 A200700

Adjacent sequences: A210192 A210193 A210194 * A210196 A210197 A210198

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved