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A185341
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Denominators of u(n) where u(n) = (u(n-1) + u(n-2)) / u(n-3), with u(1) = u(2) = u(3) = 1.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 5, 10, 6, 21, 77, 55, 145, 899, 868, 1988, 38411, 90347, 95357, 637807, 3506263, 2382501, 19519203, 649945741, 911672929, 3857971277, 130630182325, 366719420575, 764101349503, 12533062448579, 136235802233249
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OFFSET
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1,9
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LINKS
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FORMULA
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u(4 - n) = u(n) for all n in Z.
0 = u(n) * u(n+3) - u(n+1) - u(n+2) for all n in Z. - Michael Somos, Nov 01 2014
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EXAMPLE
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u(1), ... = 1, 1, 1, 2, 3, 5, 4, 3, 7/5, 11/10, 5/6, 29/21, 155/77, 224/55, 639/145, ...
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MATHEMATICA
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Denominator[RecurrenceTable[{u[1] == u[2] == u[3] == 1, u[n] == (u[n - 1] + u[n - 2])/u[n - 3]}, u, {n, 50}]] (* G. C. Greubel, Jun 27 2017 *)
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PROG
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(PARI) {u(n) = local(v = [1, 1, 1]); if( n<1, n = 4-n); if( n<4, 1, for( k=4, n, v = [v[2], v[3], (v[2] + v[3]) / v[1]]); denominator( v[3] ))};
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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