A210749 Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.

1, 3, 1, 6, 7, 1, 11, 21, 15, 1, 19, 53, 60, 31, 1, 32, 118, 191, 155, 63, 1, 53, 246, 514, 593, 378, 127, 1, 87, 489, 1261, 1863, 1683, 889, 255, 1, 142, 941, 2890, 5233, 6029, 4501, 2040, 511, 1, 231, 1767, 6311, 13527, 19026, 18068, 11543, 4599

Offset

1,2

Comments

Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (Fibonacci numbers).

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

Links

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

Formula

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

v(n,x)=(x+1)*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....1
6....7....1
11...21...15...1
19...53...60...31...1
First three polynomials u(n,x): 1, 3+ x, 6 + 7x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]    (* A210749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210750 *)

Crossrefs

Cf. A210750, A208510.

Sequence in context: A209696 A338995 A359574 * A330587 A350647 A199662

Adjacent sequences: A210746 A210747 A210748 * A210750 A210751 A210752

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 25 2012

Status

approved