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A161940
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a(n) = ((3+sqrt(2))*(5+sqrt(2))^n+(3-sqrt(2))*(5-sqrt(2))^n)/2.
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1
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3, 17, 101, 619, 3867, 24433, 155389, 991931, 6345363, 40639217, 260448821, 1669786219, 10707539307, 68670310033, 440429696269, 2824879831931, 18118915305123, 116216916916817, 745434117150341, 4781352082416619
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Fifth binomial transform of A162255.
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FORMULA
| a(n) = 10*a(n-1)-23*a(n-2) for n>1; a(0) = 3, a(1) = 17.
G.f.: (3-13*x)/(1-10*x+23*x^2).
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009: (Start)
G.f.: G=(3-13x)/(1-10x+23x^2).
Rec. rel.: a(n)=10a(n-1)-23a(n-2); a(0)=3, a(1)=17.
(End)
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MAPLE
| a[0] := 3: a[1] := 17: for n from 2 to 20 do a[n] := 10*a[n-1]-23*a[n-2] end do: seq(a[n], n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009]
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+r)*(5+r)^n+(3-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 01 2009]
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CROSSREFS
| Cf. A162255, A161939 (fourth binomial transform of A162255).
Sequence in context: A155610 A001541 A161473 * A074565 A054365 A116886
Adjacent sequences: A161937 A161938 A161939 * A161941 A161942 A161943
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
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EXTENSIONS
| 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 27 2009
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