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Search: id:A162561
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| A162561 |
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a(n) = ((4+sqrt(3))*(5+sqrt(3))^n+(4-sqrt(3))*(5-sqrt(3))^n)/2. |
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+0
2
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| 4, 23, 142, 914, 6016, 40052, 268168, 1800536, 12105664, 81444848, 548123872, 3689452064, 24835795456, 167190009152, 1125512591488, 7576945713536, 51008180122624, 343388995528448, 2311709992586752, 15562542024241664
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OFFSET
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0,1
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COMMENT
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Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.
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FORMULA
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a(n) = 10*a(n-1)-22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.
G.f.: (4-17*x)/(1-10*x+22*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 14 2009]
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CROSSREFS
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Cf. A077236, A162559, A162766.
Sequence in context: A158197 A038736 A091642 this_sequence A020079 A146964 A116881
Adjacent sequences: A162558 A162559 A162560 this_sequence A162562 A162563 A162564
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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), Jul 06 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), Jul 14 2009
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