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Search: id:A161944
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| A161944 |
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a(n) = ((4+sqrt(2))*(3+sqrt(2))^n+(4-sqrt(2))*(3-sqrt(2))^n)/4. |
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+0
3
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| 2, 7, 28, 119, 518, 2275, 10024, 44219, 195146, 861343, 3802036, 16782815, 74082638, 327016123, 1443518272, 6371996771, 28127352722, 124160138935, 548069364556, 2419295214791, 10679285736854, 47140647917587
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OFFSET
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0,1
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COMMENT
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Third binomial transform of A135530.
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FORMULA
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a(n) = 6*a(n-1)-7*a(n-2) for n>1; a(0) = 2; a(1) = 7.
G.f.: (2-5*x)/(1-6*x+7*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)*(3+r)^n+(4-r)*(3-r)^n)/4: n in [0..21] ]; [ 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, A161941 (second binomial transform of A135530).
Sequence in context: A150650 A150651 A151298 this_sequence A150652 A130655 A150653
Adjacent sequences: A161941 A161942 A161943 this_sequence A161945 A161946 A161947
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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
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