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A126570 Triangle read by rows: characteristic polynomials of nearest-neighbor tunneling matrices of N-polygons. 0
1, 1, 2, 1, 4, 3, 1, 6, 10, 5, 1, 8, 21, 20, 4, 1, 10, 36, 56, 35, 7, 1, 12, 55, 120, 126, 56, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

William G. Harter, Physics Department, University of Arkansas; personal communication.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

Triangle read by rows, characteristic polynomials (with alternate signs) of matrices of the form: 2, 1, 0, 0,...1 1, 2, 1, 0,...0 0, 1, 2, 1,...0 .. i.e. (2,2,2...) in the main diagonal, 1's in the super and subdiagonals and "1" in the upper right position.

EXAMPLE

First few rows of the triangle are:

1;

1, 2;

1, 4, 3;

1, 6, 10, 5;

1, 8, 21, 20, 4;

1, 10, 36, 56, 35, 7;

1, 12, 55, 120, 126, 56, 6;

...

Example: Charpoly of the 4 X 4 matrix [2,1,0,1; 1,2,1,0; 0,1,2,1; 0,0,1,2] = x^4 - 8*x^3 + 21*x^2 - 20*x + 4; with a root (sqrt(3)+2).

Charpoly of the 3 X 3 matrix [2,1,1; 1,2,1; 0,1,2] = x^2 - 4*x + 3 and has a root 3.6180339... = phi + 2.

CROSSREFS

Sequence in context: A172431 A053123 A107661 * A048790 A027421 A131252

Adjacent sequences:  A126567 A126568 A126569 * A126571 A126572 A126573

KEYWORD

nonn,uned,tabl

AUTHOR

Gary W. Adamson, Dec 28 2006

STATUS

approved

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Last modified October 18 03:42 EDT 2018. Contains 316304 sequences. (Running on oeis4.)