A209574 Triangle of coefficients of polynomials v(n,x) jointly generated with A209573; see the Formula section.

1, 2, 3, 3, 7, 5, 4, 14, 20, 7, 5, 24, 52, 45, 9, 6, 37, 110, 155, 86, 11, 7, 53, 203, 403, 389, 147, 13, 8, 72, 340, 882, 1240, 856, 232, 15, 9, 94, 530, 1712, 3204, 3322, 1702, 345, 17, 10, 119, 782, 3040, 7170, 10088, 7962, 3125, 490, 19, 11, 147, 1105

Offset

1,2

Comments

Combinatorial limit of row n satisfies linear recurrence

r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=3. For a

discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..58.

Formula

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

v(n,x)=2x*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...3
3...7....5
4...14...20...7
5...24...52...45...9
First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 2 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[%]   (* A209573 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209574 *)

Crossrefs

Cf. A209573, A208510.

Sequence in context: A358182 A208525 A342878 * A079387 A141061 A256447

Adjacent sequences: A209571 A209572 A209573 * A209575 A209576 A209577

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved