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Search: id:A161947
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| A161947 |
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a(n) = ((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)/4 |
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+0
2
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| 2, 11, 64, 387, 2398, 15079, 95636, 609543, 3895802, 24938531, 159781864, 1024232427, 6567341398, 42116068159, 270111829436, 1732448726703, 11111915190002, 71272831185851, 457154262488464, 2932267507610067
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Fifth binomial transform of A135530.
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FORMULA
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a(n) = 10*a(n-1)-23*a(n-2) for n>1; a(0) = 2; a(1) = 11.
G.f.: (2-9*x)/(1-10*x+23*x^2).
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009: (Start)
G.f.=(2-9x)/(1-10x+23x^2).
Rec. rel.: a(n)=10a(n-1)-23a(n-2); a(0)=2, a(1)=11.
(End)
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MAPLE
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seq(simplify(((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)*1/4), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 01 2009]
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CROSSREFS
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Cf. A135530.
Sequence in context: A080049 A126745 A038725 this_sequence A001565 A074613 A039632
Adjacent sequences: A161944 A161945 A161946 this_sequence A161948 A161949 A161950
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
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EXTENSIONS
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Edited and extended beyond a(4) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 01 2009
Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009
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