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Search: id:A161941
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| A161941 |
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a(n) = ((4+sqrt(2))*(2+sqrt(2))^n+(4-sqrt(2))*(2-sqrt(2))^n)/4. |
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+0
5
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| 2, 5, 16, 54, 184, 628, 2144, 7320, 24992, 85328, 291328, 994656, 3395968, 11594560, 39586304, 135156096, 461451776, 1575494912, 5379076096, 18365314560, 62703106048, 214081795072, 730920968192, 2495520282624, 8520239194112
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OFFSET
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0,1
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COMMENT
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Second binomial transform of A135530.
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FORMULA
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a(n) = 4*a(n-1)-2*a(n-2) for n>1; a(0) = 2; a(1) = 5.
G.f.: (2-3*x)/(1-4*x+2*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)*(2+r)^n+(4-r)*(2-r)^n)/4: n in [0..24] ]; [ 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, A161944 (third binomial transform of A135530).
Sequence in context: A081126 A006191 A149959 this_sequence A120899 A149960 A149961
Adjacent sequences: A161938 A161939 A161940 this_sequence A161942 A161943 A161944
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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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