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A010907
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Pisot sequence E(4,19), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
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2
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4, 19, 90, 426, 2016, 9541, 45154, 213697, 1011348, 4786332, 22651920, 107203069, 507352048, 2401107571, 11363544486, 53779407822, 254517831936, 1204537747753, 5700626846950, 26978935702753, 127681216679304, 604267465267128, 2859772009358880, 13534231802298265, 64052459384483260, 303136344428812723, 1434630991482656082, 6789572149788327282
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OFFSET
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0,1
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REFERENCES
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Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
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LINKS
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FORMULA
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Theorem: a(n) = 4 a(n - 1) + 3 a(n - 2) + 2 a(n - 3) + a(n - 4). (Proved using the PtoRv program of Ekhad-Sloane-Zeilberger.) - N. J. A. Sloane, Sep 09 2016
G.f.: -(x^3+2*x^2+3*x+4)/(x^4+2*x^3+3*x^2+4*x-1). [Colin Barker, Nov 29 2012] (This follows from the above recurrence. - N. J. A. Sloane, Sep 09 2016)
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MATHEMATICA
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PSE[a_, b_, n_]:=Join[{x=a, y=b}, Table[z=Floor[y^2/x+1/2]; x=y; y=z, {n}]]; A010907=PSE[4, 19, 20] (* Zak Seidov, Mar 24 2011 *)
nxt[{a_, b_}]:={b, Floor[b^2/a+1/2]}; Transpose[NestList[nxt, {4, 19}, 20]] [[1]] (* Harvey P. Dale, Mar 13 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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