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A082841
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a(n) = 4a(n-1) - a(n-2).
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6
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3, 9, 33, 123, 459, 1713, 6393, 23859, 89043, 332313, 1240209, 4628523, 17273883, 64467009, 240594153, 897909603, 3351044259, 12506267433, 46674025473, 174189834459, 650085312363, 2426151414993, 9054520347609, 33791929975443
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| y-values in the solution to 3*x^2+6=y^2. - Sture Sjöstedt, Nov 25 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: (3-6x+3x^2)/((1-x)(1-4x+x^2)). With a=2+sqrt(3), b=2-sqrt(3): a(n)=sqrt(3/2)(a^(n+1/2)+b^(n+1/2)). a(n)=sqrt(3(11+12*A082840(n)+4*A082840(n)^2)). a(n)=sqrt((3/2)(A003500(2n+1)+2)). a(n)-a(n-1)=6*A001353(n). a(n)=3 (mod 6)
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MATHEMATICA
| CoefficientList[Series[(3-6 x+3 x^2)/((1-x)(1-4 x+x^2)), {x, 0, 25}], x]
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CROSSREFS
| First differences of A005320.
Equals 3 * A001835(n+1).
A001834
Sequence in context: A148995 A148996 A148997 * A151038 A039648 A049182
Adjacent sequences: A082838 A082839 A082840 * A082842 A082843 A082844
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Apr 14 2003
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