

A210878


Triangle of coefficients of polynomials u(n,x) jointly generated with A210879; see the Formula section.


3



1, 0, 3, 0, 4, 7, 0, 2, 14, 17, 0, 2, 12, 46, 41, 0, 2, 8, 54, 140, 99, 0, 2, 8, 42, 212, 408, 239, 0, 2, 8, 34, 200, 758, 1154, 577, 0, 2, 8, 34, 160, 866, 2544, 3194, 1393, 0, 2, 8, 34, 144, 754, 3448, 8154, 8696, 3363, 0, 2, 8, 34, 144, 642, 3400, 12850
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OFFSET

1,3


COMMENTS

Leading coefficient of u(n,x): A001333
Limiting row: 0,2,8,34,144,610,...(Fibonacci numbers)
For a discussion and guide to related arrays, see A208510.


LINKS

Table of n, a(n) for n=1..63.


FORMULA

u(n,x)=x*u(n1,x)+2x*v(n1,x),
v(n,x)=(x+1)*u(n1,x)+x*v(n1,x)+1,
where u(1,x)=1, v(1,x)=1.


EXAMPLE

First six rows:
1
0...3
0...4...7
0...2...14...17
0...2...12...46...41
0...2...8....54...140...99
First three polynomials u(n,x): 1, 3x, 4x + 7x^2.


MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := x*u[n  1, x] + 2 x*v[n  1, x];
v[n_, x_] := (x + 1)*u[n  1, x] + 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[%] (* A210878 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210879 *)


CROSSREFS

Cf. A210879, A208510.
Sequence in context: A111493 A190181 A145092 * A320373 A303274 A199608
Adjacent sequences: A210875 A210876 A210877 * A210879 A210880 A210881


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Mar 30 2012


STATUS

approved



