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A284966 Triangle read by rows: coefficients of the scaled Lucas polynomials x^(n/2) L(n, sqrt(x)). 1
0, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 2, 4, 1, 0, 0, 0, 5, 5, 1, 0, 0, 0, 2, 9, 6, 1, 0, 0, 0, 0, 7, 14, 7, 1, 0, 0, 0, 0, 2, 16, 20, 8, 1, 0, 0, 0, 0, 0, 9, 30, 27, 9, 1, 0, 0, 0, 0, 0, 2, 25, 50, 35, 10, 1, 0, 0, 0, 0, 0, 0, 11, 55, 77, 44, 11, 1, 0, 0, 0, 0, 0, 0, 2, 36, 105, 112, 54, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For n >= 3, also the coefficients of the edge and vertex cover polynomials for the n-cycle graph C_n.

LINKS

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Cycle Graph

Eric Weisstein's World of Mathematics, Edge Cover Polynomial

Eric Weisstein's World of Mathematics, Lucas Polynomia

Eric Weisstein's World of Mathematics, Vertex Cover Polynomial

EXAMPLE

First few polynomials are

2

x

2 x + x^2

3 x^2 + x

2 x^2 + 4 x^3 + x^4

giving

2;

0, 1;

0, 2, 1;

0, 0, 3, 1;

0, 0, 2, 4, 1;

0, 0, 0, 5, 5, 1;

...

MATHEMATICA

CoefficientList[Table[x^(n/2) LucasL[n, Sqrt[x]], {n, 12}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)

CoefficientList[Table[2 x^n (-1/x)^(n/2) ChebyshevT[n, 1/(2 Sqrt[-1/x])], {n, 12}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)

CoefficientList[Table[FunctionExpand[2 (-(1/x))^(n/2) x^n Cos[n ArcSec[2 Sqrt[-(1/x)]]]], {n, 15}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)

CoefficientList[LinearRecurrence[{x, x}, {x, x (2 + x)}, 15], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)

CROSSREFS

Cf. A034807 (Lucas polynomials x^(n/2) L(n, 1/sqrt(x)).

Cf. A111125, A127677, A136481.

Sequence in context: A105820 A136263 A105593 * A029371 A114374 A111505

Adjacent sequences:  A284963 A284964 A284965 * A284967 A284968 A284969

KEYWORD

nonn,easy,tabl

AUTHOR

Eric W. Weisstein, Apr 06 2017

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)