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Search: id:A164303
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| A164303 |
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a(n) = ((3+4*sqrt(2))*(1+sqrt(2))^n+(3-4*sqrt(2))*(1-sqrt(2))^n)/2. |
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+0
3
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| 3, 11, 25, 61, 147, 355, 857, 2069, 4995, 12059, 29113, 70285, 169683, 409651, 988985, 2387621, 5764227, 13916075, 33596377, 81108829, 195814035, 472736899, 1141287833, 2755312565, 6651912963, 16059138491, 38770189945, 93599518381
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Binomial transform of A164654. Inverse binomial transform of A164304.
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FORMULA
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a(n) = 2*a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.
G.f.: (3+5*x)/(1-2*x-x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(1+r)^n+(3-4*r)*(1-r)^n)/2: n in [0..28] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 20 2009]
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CROSSREFS
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Cf. A164654, A164304.
Sequence in context: A118436 A056106 A147382 this_sequence A129082 A060746 A111935
Adjacent sequences: A164300 A164301 A164302 this_sequence A164304 A164305 A164306
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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), Aug 12 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 20 2009
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