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A014003 Pisot sequence E(9,15), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ). 1
9, 15, 25, 42, 71, 120, 203, 343, 580, 981, 1659, 2806, 4746, 8027, 13576, 22961, 38834, 65680, 111085, 187879, 317761, 537431, 908960, 1537329, 2600093, 4397552, 7437605, 12579264, 21275381, 35983173, 60858545, 102930403, 174086776, 294433954, 497977820 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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.
FORMULA
Known not to satisfy any linear recurrence.
MATHEMATICA
nxt[{a_, b_}]:={b, Floor[b^2/a+1/2]}; NestList[nxt, {9, 15}, 40][[All, 1]] (* Harvey P. Dale, Jan 31 2023 *)
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, 9, 15) \\ Colin Barker, Jul 28 2016
CROSSREFS
Sequence in context: A251415 A109888 A193227 * A333788 A082549 A013569
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)