A048583 -id:A048583 - cp's OEIS frontend

A048586 Pisot sequence L(6,8).

6, 8, 11, 16, 24, 36, 54, 81, 122, 184, 278, 421, 638, 967, 1466, 2223, 3371, 5112, 7753, 11759, 17835, 27051, 41030, 62233, 94394, 143176, 217169, 329402, 499638, 757853, 1149515, 1743590, 2644686, 4011473, 6084623, 9229188, 13998881, 21233577, 32207203

Offset: 0

David W. Wilson

nonn

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for Pisot sequences

Subsequence of A048583. See A008776 for definitions of Pisot sequences.

L := proc(a0,a1,n)
    option remember;
    if n = 0 then
        a0 ;
    elif n = 1 then
        a1;
    else
        ceil( procname(a0,a1,n-1)^2/procname(a0,a1,n-2)) ;
    end if;
end proc:
A048586 := proc(n)
    L(6,8,n) ;
end proc: # R. J. Mathar, Feb 12 2016

L[a0_, a1_, n_] := L[a0, a1, n] = Switch[n, 0, a0, 1, a1, _, Ceiling[L[a0, a1, n-1]^2/L[a0, a1, n-2]]];
a[n_] := L[6, 8, n];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 25 2023, after R. J. Mathar *)

pisotL(nmax, a1, a2) = {
  a=vector(nmax); a[1]=a1; a[2]=a2;
  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));
  a
}
pisotL(50, 6, 8) \\ Colin Barker, Aug 07 2016

A277088 Pisot sequences L(5,12), S(5,12).

Original entry on oeis.org

5, 12, 29, 71, 174, 427, 1048, 2573, 6318, 15514, 38095, 93544, 229702, 564045, 1385042, 3401044, 8351444, 20507414, 50357044, 123654396, 303639937, 745603993, 1830870208, 4495799044, 11039673351, 27108504296, 66566372193, 163457262657, 401377990645

Offset: 0

Ilya Gutkovskiy, Sep 29 2016

Ilya Gutkovskiy, Pisot sequences L(x,y)
Index entries for Pisot sequences

Cf. A008776 for definitions of Pisot sequences.
Cf. A000129 (with offset 3 appears to be Pisot sequences E(5,12), P(5,12)).
Cf. A020736, A020737, A048583.

RecurrenceTable[{a[0] == 5, a[1] == 12, a[n] == Ceiling[a[n - 1]^2/a[n - 2]]}, a, {n, 28}]
RecurrenceTable[{a[0] == 5, a[1] == 12, a[n] == Floor[a[n - 1]^2/a[n - 2] + 1]}, a, {n, 28}]

a(n) = ceiling(a(n-1)^2/a(n-2)), a(0) = 5, a(1) = 12.
a(n) = floor(a(n-1)^2/a(n-2)+1), a(0) = 5, a(1) = 12.
Conjectures: (Start)
G.f.: (5 - 3*x + 3*x^2 - 2*x^3 + x^5 - 3*x^6 - x^7 - 2*x^8)/((1 - x)*(1 - 2*x - 2*x^3 - x^4 - x^5 - 2*x^6 - x^7 - x^8)).
a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) - a(n-7) - a(n-9). (End)

cp's OEIS Frontend

A048586 Pisot sequence L(6,8).

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