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%I #13 Jun 28 2018 04:49:47
%S 0,1,1,1,7,1,5,47,53,23,259,577,715,839,4301,8591,3557,22249,73795,
%T 95137,38357,481127,1051949,821807,2064955,8376649,13307491,917761,
%U 49342133,129187079,134693645,161359153,936481627,1744643497,776488579
%N a(n) = |b(n)| where b(n) = -b(n-1) + 6*b(n-3) with b(0)=0, b(1)=1, b(2)=1.
%C Original name was: Sequence obtained using characteristic polynomial that is Laplace transform of the minimal Pisot characteristic polynomial: -s^4*L(t^3-t-1) = s^3 + s^2-6.
%H Robert Israel, <a href="/A107786/b107786.txt">Table of n, a(n) for n = 0..3380</a>
%F G.f. of b(n): (x+2*x^2)/(1+x-6*x^3). - _Robert Israel_, Jun 27 2018
%p f:= gfun:-rectoproc({a(n) = -a(n-1)+6*a(n-3),a(0)=0,a(1)=1,a(2)=1},a(n),remember):
%p map(abs@f, [$0..50]); # _Robert Israel_, Jun 27 2018
%t (* first method *) F[1] = 0; F[2] = 1; F[3] = 1; F[n__] := F[n] = -F[n - 1] + 6*F[n - 3] a = Table[Abs[F[n]], {n, 1, 50}] (*second method*) M = {{0, 1, 0}, {0, 0, 1}, {6, 0, -1}} v[1] = {0, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[3]]
%t Abs[LinearRecurrence[{-1, 0, 6}, {0, 1, 1}, 40]] (* _Vincenzo Librandi_, Jun 28 2016 *)
%K nonn
%O 0,5
%A _Roger L. Bagula_, Jun 11 2005
%E Edited by _Robert Israel_, Jun 27 2018
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