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A131589
Expansion of -(3+9*x+2*x^2)/((x+1)*(x^2+3*x+1)).
1
-3, 3, -2, -1, 9, -30, 85, -229, 606, -1593, 4177, -10942, 28653, -75021, 196414, -514225, 1346265, -3524574, 9227461, -24157813, 63245982, -165580137, 433494433, -1134903166, 2971215069, -7778742045, 20365011070, -53316291169, 139583862441, -365435296158, 956722026037
OFFSET
0,1
COMMENTS
Floretion Algebra Multiplication Program, FAMP Code: 2tesforseq[A*B], with A = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = + .5'ij' + .5'ji'; 1vesforseq(n) = (-1)^(n+1)*2, ForType: 1A
FORMULA
a(n) + a(n+1) = (-1)^(n+1)*A001906(n) = (-1)^(n+1)*F(2n).
From Colin Barker, May 01 2019: (Start)
a(n) = -(2^(-1-n)*(5*(-1)^n*2^(3+n) + (-3-sqrt(5))^n*(-5+sqrt(5)) - (-3+sqrt(5))^n*(5+sqrt(5)))) / 5.
a(n) = -4*a(n-1) - 4*a(n-2) - a(n-3) for n>2. (End)
MATHEMATICA
CoefficientList[Series[-(3+9x+2x^2)/((x+1)(x^2+3x+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{-4, -4, -1}, {-3, 3, -2}, 40] (* Harvey P. Dale, Jun 22 2022 *)
PROG
(PARI) Vec(-(3 + 9*x + 2*x^2) / ((1 + x)*(1 + 3*x + x^2)) + O(x^35)) \\ Colin Barker, May 01 2019
CROSSREFS
Cf. A001906.
Sequence in context: A175644 A102905 A020862 * A338113 A309119 A308725
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Aug 30 2007
EXTENSIONS
Definition corrected (by negating prior formula) by Harvey P. Dale, Jun 22 2022
STATUS
approved