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 A147962 #24 Sep 08 2022 08:45:38 %S A147962 1,7,52,406,3292,27412,232336,1991752,17197072,149138416,1296872512, %T A147962 11295848032,98485736896,859191307072,7498334401792,65453881499776, %U A147962 571430958514432,4989154870212352,43562344091309056,380371693248558592,3321335877279603712 %N A147962 a(n) = ((7+sqrt(3))^n + (7-sqrt(3))^n) / 2. %H A147962 Colin Barker, <a href="/A147962/b147962.txt">Table of n, a(n) for n = 0..1000</a> %H A147962 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14, -46). %F A147962 From _Zak Seidov_, Nov 19 2008: (Start) %F A147962 a(0) = 1; a(1) = 7; a(n) = 14 * a(n - 1) - 46 * a(n - 2); %F A147962 a(n) = ((7+sqrt(3))^n + (7-sqrt(3))^n)/2. (End) %F A147962 From _Philippe Deléham_, Nov 19 2008: (Start) %F A147962 G.f.: (1-7*x)/(1-14*x+46*x^2). %F A147962 a(n) = (Sum_{k=0..n} A098158(n,k)*7^(2*k)*3^(n-k))/7^n. (End) %t A147962 LinearRecurrence[{14,-46},{1,7},30] (* _Harvey P. Dale_, Aug 18 2012 *) %o A147962 (Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((7+r3)^n+(7-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 19 2008 %o A147962 (PARI) Vec((1-7*x) / (1-14*x+46*x^2) + O(x^30)) \\ _Colin Barker_, Sep 24 2017 %K A147962 nonn,easy %O A147962 0,2 %A A147962 Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008 %E A147962 Extended beyond a(6) by _Klaus Brockhaus_ and _Zak Seidov_, Nov 19 2008