A210558 Triangle of coefficients of polynomials v(n,x) jointly generated with A210557; see the Formula section.

1, 2, 3, 3, 7, 7, 4, 12, 20, 17, 5, 18, 40, 57, 41, 6, 25, 68, 129, 158, 99, 7, 33, 105, 243, 399, 431, 239, 8, 42, 152, 410, 824, 1200, 1160, 577, 9, 52, 210, 642, 1506, 2692, 3528, 3089, 1393, 10, 63, 280, 952, 2532, 5290, 8536, 10185, 8154, 3363, 11

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..56.

Formula

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

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...7
4...12...20...17
5...18...40...57...41
First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^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_] := 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[%]   (* A210557 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210558 *)

Crossrefs

Cf. A210557, A208510.

Sequence in context: A171824 A143444 A108346 * A208920 A210234 A209768

Adjacent sequences: A210555 A210556 A210557 * A210559 A210560 A210561

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 22 2012

Status

approved