This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163064 #9 Sep 08 2022 08:45:46 %S A163064 3,17,103,637,3963,24697,153983,960197,5987763,37339937,232854103, %T A163064 1452093517,9055353003,56469795337,352149479663,2196028088597, %U A163064 13694580432483,85400334485297,532562291125063,3321094649662237 %N A163064 a(n) = ((3+sqrt(5))*(4+sqrt(5))^n + (3-sqrt(5))*(4-sqrt(5))^n)/2. %C A163064 Binomial transform of A098648 without initial 1. Fourth binomial transform of A163114. Inverse binomial transform of A163065. %H A163064 G. C. Greubel, <a href="/A163064/b163064.txt">Table of n, a(n) for n = 0..1000</a> %H A163064 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-11). %F A163064 a(n) = 8*a(n-1) - 11*a(n-2) for n > 1; a(0) = 3, a(1) = 17. %F A163064 G.f.: (3-7*x)/(1-8*x+11*x^2). %t A163064 CoefficientList[Series[(3-7*x)/(1-8*x+11*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{8,-11}, {3,17}, 30] (* _G. C. Greubel_, Dec 22 2017 *) %o A163064 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 21 2009 %o A163064 (Magma) I:=[3,17]; [n le 2 select I[n] else 8*Self(n-1) - 11*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Dec 22 2017 %o A163064 (PARI) x='x+O('x^30); Vec((3-7*x)/(1-8*x+11*x^2)) \\ _G. C. Greubel_, Dec 22 2017 %Y A163064 Cf. A098648, A163114, A163065. %K A163064 nonn %O A163064 0,1 %A A163064 Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009 %E A163064 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 21 2009