Search: id:A161940
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%I A161940
%S A161940 3,17,101,619,3867,24433,155389,991931,6345363,40639217,260448821,
%T A161940 1669786219,10707539307,68670310033,440429696269,2824879831931,
%U A161940 18118915305123,116216916916817,745434117150341,4781352082416619
%N A161940 a(n) = ((3+sqrt(2))*(5+sqrt(2))^n+(3-sqrt(2))*(5-sqrt(2))^n)/2.
%C A161940 Fifth binomial transform of A162255.
%F A161940 a(n) = 10*a(n-1)-23*a(n-2) for n>1; a(0) = 3, a(1) = 17.
%F A161940 G.f.: (3-13*x)/(1-10*x+23*x^2).
%F A161940 Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009: 
               (Start)
%F A161940 G.f.: G=(3-13x)/(1-10x+23x^2).
%F A161940 Rec. rel.: a(n)=10a(n-1)-23a(n-2); a(0)=3, a(1)=17.
%F A161940 (End)
%p A161940 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]
%o A161940 (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]
%Y A161940 Cf. A162255, A161939 (fourth binomial transform of A162255).
%Y A161940 Sequence in context: A056660 A155610 A001541 this_sequence A074565 A054365 
               A116886
%Y A161940 Adjacent sequences: A161937 A161938 A161939 this_sequence A161941 A161942 
               A161943
%K A161940 nonn
%O A161940 0,1
%A A161940 Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
%E A161940 Edited and extended beyond a(4) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jul 01 2009
%E A161940 Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009

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