

A126570


Triangle read by rows: characteristic polynomials of nearestneighbor tunneling matrices of Npolygons.


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
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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



