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Search: id:A123972
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| A123972 |
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a(n) = 1 - 2*n - n^2 + n^3. |
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+0
1
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| 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)
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OFFSET
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0,4
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COMMENT
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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)
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MAPLE
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with(linalg): M:=n->matrix(3, 3, [n, -1, 0, -1, n, -1, 0, -1, n-1]): seq(det(M(n)), n=0..42);
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MATHEMATICA
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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}]
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CROSSREFS
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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
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KEYWORD
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sign
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 30 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2006 and Nov 24 2006
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