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A285072 Triangle read by rows: coefficients of the Laplacian polynomial of the n-path graph P_n. 1
0, -1, 0, -2, 1, 0, -3, 4, -1, 0, -4, 10, -6, 1, 0, -5, 20, -21, 8, -1, 0, -6, 35, -56, 36, -10, 1, 0, -7, 56, -126, 120, -55, 12, -1, 0, -8, 84, -252, 330, -220, 78, -14, 1, 0, -9, 120, -462, 792, -715, 364, -105, 16, -1, 0, -10, 165, -792, 1716, -2002, 1365, -560, 136, -18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Version of A053122 with row-leading 0s and differing signs.

LINKS

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Path Graph

Eric Weisstein's World of Mathematics, Laplacian Polynomial

MATHEMATICA

CoefficientList[Table[CharacteristicPolynomial[KirchhoffMatrix[PathGraph[Range[n]]], x], {n, 10}], x] // Flatten (* Eric W. Weisstein, Apr 09 2017 *)

CoefficientList[LinearRecurrence[{2 - x, -1}, {-x, (-2 + x) x}, 10], x] // Flatten (* Eric W. Weisstein, Apr 09 2017 *)

CoefficientList[Table[(-1)^(n + 1) x^(1/2) ChebyshevU[2 n - 1, -Sqrt[x]/2], x] // Flatten (* Eric W. Weisstein, Apr 09 2017 *)

CoefficientList[Table[(2^-n ((2 - Sqrt[-4 + x] Sqrt[x] - x)^n - (2 + Sqrt[-4 + x] Sqrt[x] - x)^n))/Sqrt[(-4 + x)/x], {n, 10}] // Expand // FullSimplify, x] // Flatten (* Eric W. Weisstein, Apr 09 2017 *)

CROSSREFS

Cf. A053122 (version lacking row-leading 0s and with differing signs).

Sequence in context: A268830 A095884 A128908 * A300454 A155112 A256130

Adjacent sequences:  A285069 A285070 A285071 * A285073 A285074 A285075

KEYWORD

sign,easy,tabl

AUTHOR

Eric W. Weisstein, Apr 09 2017

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)