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A020718
Pisot sequences E(6,10), P(6,10).
1
6, 10, 17, 29, 49, 83, 141, 240, 409, 697, 1188, 2025, 3452, 5885, 10033, 17105, 29162, 49718, 84764, 144514, 246382, 420057, 716156, 1220976, 2081645, 3549002, 6050703, 10315860, 17587538, 29985042, 51121581, 87157325, 148594765, 253339627, 431919433
OFFSET
0,1
LINKS
Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT], 2016.
FORMULA
G.f.: (-4*x^5+x^4+x^3-3*x^2-2*x+6)/((1-x)*(1-x-x^2-x^5)) (conjectured). - Ralf Stephan, May 12 2004
a(n) = 2*a(n-1)-a(n-3)+a(n-5)-a(n-6) for n>5 (conjectured). - Colin Barker, Jun 05 2016
Theorem: E(6,10) satisfies a(n) = 2 a(n - 1) - a(n - 3) + a(n - 5) - a(n - 6) for n >= 6. Proved using the PtoRv program of Ekhad-Sloane-Zeilberger. This shows that the above conjectures are correct. - N. J. A. Sloane, Sep 10 2016
MATHEMATICA
LinearRecurrence[{2, 0, -1, 0, 1, -1}, {6, 10, 17, 29, 49, 83}, 30] (* Jinyuan Wang, Mar 10 2020 *)
CROSSREFS
See A008776 for definitions of Pisot sequences.
Sequence in context: A315357 A315358 A049302 * A048587 A351661 A116001
KEYWORD
nonn
STATUS
approved