OFFSET
1,4
COMMENTS
Extended to n = 1 and n = 2 using the closed form.
Closely related to A127677, which has opposite signs and rows begin with 2 of alternating signs instead of 0.
LINKS
Eric Weisstein's World of Mathematics, Cycle Graph
Eric Weisstein's World of Mathematics, Laplacian Polynomial
EXAMPLE
First few polynomials are
-x
-4*x + x^2
-9*x + 6*x^2 - x^3
which give the triangle of coefficients:
0, -1;
0, -4, 1;
0, -9, 6, -1;
...
MATHEMATICA
CoefficientList[LucasL[2 Range[10], Sqrt[-x]] - 2, x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)
CoefficientList[2 (ChebyshevT[Range[10], 1 - x/2] - 1), x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)
CoefficientList[FunctionExpand[2 (Cos[Range[10] ArcCos[1 - x/2]] - 1)], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)
CoefficientList[LinearRecurrence[{3 - x, -3 + x, 1}, {-x, (-4 + x) x, -(-3 + x)^2 x}, 10], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Eric W. Weisstein, Apr 06 2017
STATUS
approved