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A020746 Pisot sequence T(3,7), a(n) = floor(a(n-1)^2/a(n-2)). 3
3, 7, 16, 36, 81, 182, 408, 914, 2047, 4584, 10265, 22986, 51471, 115255, 258081, 577899, 1294040, 2897633, 6488421, 14528964, 32533461, 72849384, 163125366, 365272615, 817923579, 1831505986, 4101133972, 9183316890, 20563412382, 46045882316, 103106587509 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

D. W. Boyd, Pisot sequences which satisfy no linear recurrences, Acta Arith. 32 (1) (1977) 89-98

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305

D. W. Boyd, On linear recurrence relations satisfied by Pisot sequences, Acta Arithm. 47 (1) (1986) 13

D. W. Boyd, Pisot sequences which satisfy no linear recurrences. II, Acta Arithm. 48 (1987) 191

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.

D. G. Cantor, On families of Pisot E-sequences, Ann. Sci. Ecole Nat. Sup. 9 (2) (1976) 283-308

FORMULA

Conjectured g.f.: (-x^5+x^4-x^3+x^2-2*x+3)/((1-x)*(1-2*x-x^3-x^5)). - Ralf Stephan, May 12 2004

I believe that David Boyd has proved that this g.f. is correct. - N. J. A. Sloane, Aug 11 2016

MATHEMATICA

RecurrenceTable[{a[0] == 3, a[1] == 7, a[n] == Floor[a[n - 1]^2/a[n - 2]]}, a, {n, 0, 40}] (* Bruno Berselli, Feb 04 2016 *)

PROG

(MAGMA) Iv:=[3, 7]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // Bruno Berselli, Feb 04 2016

(PARI) pisotT(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]));

  a

}

pisotT(50, 3, 7) \\ Colin Barker, Jul 29 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Cf. A010919, A010925.

Sequence in context: A019489 A077852 A218983 * A033303 A078056 A173761

Adjacent sequences:  A020743 A020744 A020745 * A020747 A020748 A020749

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 29 01:54 EST 2020. Contains 331328 sequences. (Running on oeis4.)