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A020717
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Pisot sequences L(6,9), E(6,9).
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3
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6, 9, 14, 22, 35, 56, 90, 145, 234, 378, 611, 988, 1598, 2585, 4182, 6766, 10947, 17712, 28658, 46369, 75026, 121394, 196419, 317812, 514230, 832041, 1346270, 2178310, 3524579, 5702888, 9227466, 14930353, 24157818, 39088170, 63245987, 102334156, 165580142
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OFFSET
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0,1
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REFERENCES
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Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, Preprint, 2016.
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LINKS
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FORMULA
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a(n) = Fibonacci(n+5)+1 = A001611(n+5).
a(n) = 2*a(n-1) - a(n-3).
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MATHEMATICA
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PROG
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(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
}
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CROSSREFS
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See A008776 for definitions of Pisot sequences.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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