A020718 Pisot sequences E(6,10), P(6,10).

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

Colin Barker, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,0,1,-1).

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 A379166

Adjacent sequences: A020715 A020716 A020717 * A020719 A020720 A020721

Keyword

nonn

Author

David W. Wilson

Status

approved