# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a164603 Showing 1-1 of 1 %I A164603 #20 Sep 08 2022 08:45:47 %S A164603 1,18,76,376,1808,8736,42176,203648,983296,4747776,22924288,110688256, %T A164603 534450176,2580553728,12460015616,60162277376,290489171968, %U A164603 1402605797376,6772379877376,32699942699008,157889290305536 %N A164603 a(n) = ((1+4*sqrt(2))*(2+2*sqrt(2))^n + (1-4*sqrt(2))*(2-2*sqrt(2))^n)/2. %C A164603 Binomial transform of A164602. Second binomial transform of A164702. Inverse binomial transform of A164604. %H A164603 G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..164 from Vincenzo Librandi) %H A164603 Index entries for linear recurrences with constant coefficients, signature (4,4). %F A164603 a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 18. %F A164603 G.f.: (1+14*x)/(1-4*x-4*x^2). %F A164603 E.g.f.: exp(2*x)*( cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x) ). - _G. C. Greubel_, Aug 11 2017 %t A164603 CoefficientList[Series[(-1-14 n)/(-1+4 n+4 n^2),{n,0,20}],n] (* _Harvey P. Dale_, Feb 22, 2011 *) %o A164603 (Magma) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+4*r)*(2+2*r)^n+(1-4*r)*(2-2*r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 23 2009 %o A164603 (PARI) Vec((1+14*x)/(1-4*x-4*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 12 2011 %Y A164603 Cf. A164602, A164702, A164604. %K A164603 nonn,easy %O A164603 0,2 %A A164603 Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009 %E A164603 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 23 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE