Search: id:A161947
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%I A161947
%S A161947 2,11,64,387,2398,15079,95636,609543,3895802,24938531,159781864,
%T A161947 1024232427,6567341398,42116068159,270111829436,1732448726703,
%U A161947 11111915190002,71272831185851,457154262488464,2932267507610067
%N A161947 a(n) = ((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)/4
%C A161947 Fifth binomial transform of A135530.
%F A161947 a(n) = 10*a(n-1)-23*a(n-2) for n>1; a(0) = 2; a(1) = 11.
%F A161947 G.f.: (2-9*x)/(1-10*x+23*x^2).
%F A161947 Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009: 
               (Start)
%F A161947 G.f.=(2-9x)/(1-10x+23x^2).
%F A161947 Rec. rel.: a(n)=10a(n-1)-23a(n-2); a(0)=2, a(1)=11.
%F A161947 (End)
%p A161947 seq(simplify(((4+sqrt(2))*(5+sqrt(2))^n+(4-sqrt(2))*(5-sqrt(2))^n)*1/
               4), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jun 28 2009]
%o A161947 (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ 
               ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: 
               j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jul 01 2009]
%Y A161947 Cf. A135530.
%Y A161947 Sequence in context: A080049 A126745 A038725 this_sequence A001565 A074613 
               A039632
%Y A161947 Adjacent sequences: A161944 A161945 A161946 this_sequence A161948 A161949 
               A161950
%K A161947 nonn
%O A161947 0,1
%A A161947 Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
%E A161947 Edited and extended beyond a(4) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jul 01 2009
%E A161947 Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009

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