A210217 Triangle of coefficients of polynomials u(n,x) jointly generated with A210218; see the Formula section.

1, 2, 1, 2, 5, 1, 2, 6, 12, 1, 2, 6, 19, 27, 1, 2, 6, 20, 57, 58, 1, 2, 6, 20, 67, 160, 121, 1, 2, 6, 20, 68, 218, 424, 248, 1, 2, 6, 20, 68, 231, 680, 1073, 503, 1, 2, 6, 20, 68, 232, 775, 2028, 2619, 1014, 1, 2, 6, 20, 68, 232, 791, 2543, 5797, 6214, 2037, 1, 2

Offset

1,2

Comments

Limiting row: A006012

Row sums: even-indexed Fibonacci numbers: 1,3,8,21,...

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

Links

Table of n, a(n) for n=1..67.

Formula

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

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

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

Example

First five rows:
1
2...1
2...5...1
2...6...12...1
2...6...19...27...1
First three polynomials u(n,x): 1, 2 + x, 2 + 5x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 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[%]    (* A210217 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210218 *)

Crossrefs

Cf. A210218, A208510.

Sequence in context: A132309 A144224 A122881 * A334165 A370887 A210223

Adjacent sequences: A210214 A210215 A210216 * A210218 A210219 A210220

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 19 2012

Status

approved