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 A014001 Pisot sequence E(7,15), a(n)=[ a(n-1)^2/a(n-2)+1/2 ]. 1
 7, 15, 32, 68, 145, 309, 658, 1401, 2983, 6351, 13522, 28790, 61297, 130508, 277866, 591608, 1259600, 2681830, 5709918, 12157058, 25883745, 55109407, 117334132, 249817577, 531889747, 1132453154, 2411120262, 5133546494, 10929898447, 23270984338, 49546545623 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 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. FORMULA Known not to satisfy any linear recurrence. There are linear recurrences which match e.g. the first 21 terms, but after a while they always fail. - N. J. A. Sloane, Aug 07 2016 MAPLE PisotE := proc(a0, a1, n)     option remember;     if n = 0 then         a0 ;     elif n = 1 then         a1;     else         floor( procname(a0, a1, n-1)^2/procname(a0, a1, n-2)+1/2) ;     end if; end proc: A014001 := proc(n)     PisotE(7, 15, n) ; end proc: # R. J. Mathar, Feb 12 2016 MATHEMATICA a[0] = 7; a[1] = 15; a[n_] := a[n] = Floor[a[n-1]^2/a[n-2] + 1/2]; a /@ Range[0, 30] (* Jean-François Alcover, Apr 03 2020 *) PROG (PARI) pisotE(nmax, a1, a2) = {   a=vector(nmax); a[1]=a1; a[2]=a2;   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));   a } pisotE(50, 7, 15) \\ Colin Barker, Jul 27 2016 CROSSREFS Sequence in context: A078485 A233297 A159695 * A291642 A271995 A174792 Adjacent sequences:  A013998 A013999 A014000 * A014002 A014003 A014004 KEYWORD nonn AUTHOR Simon Plouffe, Dec 11 1996 STATUS approved

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)