%I A123968
%S A123968 2,1,6,13,22,33,46,61,78,97,118,141,166,193,222,253,286,321,358,397,438,
%T A123968 481,526,573,622
%V A123968 -2,1,6,13,22,33,46,61,78,97,118,141,166,193,222,253,286,321,358,397,438,
               481,526,573,
%W A123968 622
%N A123968 Coefficient of quadratic factor of n centered 5 X 5 tridiagonal matric 
               characteristic polynomial: p(n,x)=(x-(n-1))*(x-n)*(x-(n+1)*(x^2-2*n*x+a(n)).
%C A123968 Chromatic polynomials are embedded in these characteristic polynomials. 
               The quadratic is a simple beta integer sequence: Table[ NSolve[(-3 
               + n^2 - 2 n x + x^2) == 0, x][[2]], {n, 1, 25}] has roots: n+Sqrt[3]
%C A123968 Is this a shifted version of A028872? - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 18 2008
%F A123968 M(n)={{n, -1, 0, 0, 0}, {-1, n, -1, 0, 0}, {0, -1, n, -1, 0}, {0, 0, 
               -1, n, -1}, {0, 0, 0, -1, m}}; p(n,x)=Factor(CharacteristicPolynomial(M(n)))=(-1 
               + n - x)((n - x)(1 + n - x)(-3 + n^2 - 2 n x + x^2) a(n)=n^2-3
%e A123968 A quadratic set with interesting roots.
%e A123968 1->x^2-2*x-2
%e A123968 2->x^2-4*x+1
%e A123968 3->x^2-6*x-6
%e A123968 4->13 - 8 x + x^2
%e A123968 5->22 - 10 x + x^2
%e A123968 6->33 - 12 x + x^2
%p A123968 with(combinat):seq(fibonacci(3, i)-4,i=1..55); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 20 2008
%t A123968 M[n_] := {{n, -1, 0, 0, 0}, {-1, n, -1, 0, 0}, {0, -1, n, -1, 0}, {0, 
               0, -1, n, -1}, {0, 0, 0, -1, n}}; p[n_, x_] = Factor[CharacteristicPolynomial[M[n], 
               x]] Table[ -3 + n^2, {n, 1, 25}]
%Y A123968 Sequence in context: A128534 A002562 A136456 this_sequence A068797 A049951 
               A025263
%Y A123968 Adjacent sequences: A123965 A123966 A123967 this_sequence A123969 A123970 
               A123971
%K A123968 uned,probation,sign
%O A123968 1,1
%A A123968 Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 29 2006