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A010907 Pisot sequence E(4,19), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
LINKS
D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
S. B. Ekhad, N. J. A. Sloane, D. Zeilberger, Automated proofs (or disproofs) of linear recurrences satisfied by Pisot Sequences, arXiv:1609.05570 [math.NT] (2016)
FORMULA
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)
MATHEMATICA
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 *)
CROSSREFS
Cf. A077922.
Sequence in context: A256959 A181880 A291016 * A229242 A087449 A004253
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)