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A084069
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Numbers n such that 7*n^2 = floor(n*sqrt(7)*ceil(n*sqrt(7))).
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3
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1, 3, 17, 48, 271, 765, 4319, 12192, 68833, 194307, 1097009, 3096720, 17483311, 49353213, 278635967, 786554688, 4440692161, 12535521795, 70772438609, 199781794032, 1127918325583, 3183973182717, 17975920770719, 50743789129440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,16,0,-1).
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FORMULA
| a(1)=1, a(2)=3, a(2n)=6*a(2n-1)-a(2n-2); a(2n+1)=3*a(2n)-a(2n-1)
a(n)a(n+3) = -3 + a(n+1)a(n+2).
G.f.: x*(1+3*x+x^2)/(1-16*x^2+x^4).
a(n)=16*a(n-2)-a(n-4), n>4. [From Harvey P. Dale, Oct 31 2011]
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MATHEMATICA
| CoefficientList[Series[(1+3x+x^2)/(1-16x^2+x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 16, 0, -1}, {1, 3, 17, 48}, 31] (* From Harvey P. Dale, Oct 31 2011 *)
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CROSSREFS
| Cf. A159678, A001080, A001653, A001353, A060645, A001078, A001109, A084068, A084070.
Sequence in context: A095697 A154304 A144640 * A132124 A011917 A018691
Adjacent sequences: A084066 A084067 A084068 * A084070 A084071 A084072
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
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EXTENSIONS
| Corrected formula for generating function [Harvey P. Dale, Oct 31 2011]
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