A210550 Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.

1, 2, 2, 2, 6, 4, 2, 7, 16, 8, 2, 7, 23, 40, 16, 2, 7, 24, 71, 96, 32, 2, 7, 24, 81, 207, 224, 64, 2, 7, 24, 82, 266, 575, 512, 128, 2, 7, 24, 82, 279, 843, 1535, 1152, 256, 2, 7, 24, 82, 280, 939, 2572, 3967, 2560, 512, 2, 7, 24, 82, 280, 955, 3102, 7565, 9983

Offset

1,2

Comments

Row sums: -1+odd-indexed Fibonacci numbers

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

Links

Table of n, a(n) for n=1..64.

Formula

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

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

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

Example

First five rows:
2
2...2
2...6...4
2...7...16....8
2...7...28....40...16
First three polynomials v(n,x): 2, 2 + 2x , 2 + 6x + 4x^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_] := 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[%]    (* A210549 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A210550 *)

Crossrefs

Cf. A210549, A208510.

Sequence in context: A158524 A054274 A053695 * A208659 A209752 A119918

Adjacent sequences: A210547 A210548 A210549 * A210551 A210552 A210553

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 22 2012

Status

approved