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A123972 a(n) = 1 - 2*n - n^2 + n^3. +0
1
1, -1, 1, 13, 41, 91, 169, 281, 433, 631, 881, 1189, 1561, 2003, 2521, 3121, 3809, 4591, 5473, 6461, 7561, 8779, 10121, 11593, 13201, 14951, 16849, 18901, 21113, 23491, 26041, 28769, 31681, 34783, 38081, 41581, 45289, 49211, 53353, 57721, 62321, 67159, 72241 (list; graph; listen)
OFFSET

0,4

COMMENT

a(n) = determinant of the 3 X 3 matrix {{n,-1,0 },{-1,n,-1},{0,-1,n-1}}.

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 23 2009: (Start)

for n>1, let a = 2*Cos 2Pi/7, b = 2*Cos 2*2Pi/7, c = 2*Cos 3*2Pi/7;

a = 1.24697..., b = -.44504..., c = -1.802937...; then a(n) =

(n + a) * (n + b) * (n + c). Example: a(4) = 41 = (5.246...)*(3.5495...)

* (2.19806...). Cf. 3-rd column from the left in the array of A162997. (End)

MAPLE

with(linalg): M:=n->matrix(3, 3, [n, -1, 0, -1, n, -1, 0, -1, n-1]): seq(det(M(n)), n=0..42);

MATHEMATICA

M[n_] := {{n, -1, 0 }, {-1, n, -1}, {0, -1, n - 1}}; p[n_, x_] = Factor[CharacteristicPolynomial[M[n], x]]; Table[CoefficientList[p[n, x], x][[1]], {n, 1, 25}]

CROSSREFS

A162997 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 23 2009]

Sequence in context: A102083 A139866 A026918 this_sequence A167585 A141970 A167240

Adjacent sequences: A123969 A123970 A123971 this_sequence A123973 A123974 A123975

KEYWORD

sign

AUTHOR

Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 30 2006

EXTENSIONS

Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2006 and Nov 24 2006

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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