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Search: id:A085293
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| 2, 18, 56, 238, 902, 3564, 13862, 54238, 211736, 827298, 3231362, 12623044, 49308482, 192613698, 752401496, 2939092798, 11480914982, 44847668844, 175187526662, 684331472398, 2673190054136, 10442227799538, 40790261396162
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OFFSET
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1,1
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COMMENT
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Convergent a(n+1)/a(n) = [(1+sqrt5)/2]*(1+sqrt2) = (1.618...)*(2.414213...) = 3.9062796...= (1 + sqrt2 + sqrt5 + sqrt10)/2; (since with large n, A000204 is approximated by PHI^n & A002203 is approximated by (1+sqrt2)^n, with the fractional part of each becoming negligible as n approaches infinity. Check: a(11)/a(10) = 3231362/827298 = 3.9059226...
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REFERENCES
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Gary W. Adamson
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FORMULA
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1. a(n) = [A000204(n)]*[A002203(n)], n>0. 2. a(n) = 2*[A085292(n)] 3. a(n) = [((1+sqrt5)/2)^n + ((1-sqrt5)/2)^n]*[(1+sqrt2)^n + (1-sqrt2)^n].
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EXAMPLE
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1. a(4) = 238 = [A000204(4)]*[A002203(4)] = (7)(34); where 7 = L4 in the Lucas series: 1, 3, 4, 7...; & A002203 = 2, 6, 14, 34, 82, 198, 478...
2. a(4) = 238 = (2)(119) = (2)[A085292(4)]
3. A000204(4) = 7 = [(1+sqrt5/2)]^4 + [(1-sqrt5)/2)^4]; A002203(4) = 34 = (1+sqrt2)^4 + (1-sqrt2)^4; & A085293(4) = (7)(34) = 238.
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CROSSREFS
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Cf. A085292, A000204, A002203.
Sequence in context: A058794 A121670 A114109 this_sequence A119118 A078837 A112365
Adjacent sequences: A085290 A085291 A085292 this_sequence A085294 A085295 A085296
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 24 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jan 31 2005
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