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 A147961 #24 Apr 24 2025 11:19:32
%S A147961 1,6,39,270,1953,14526,109863,838998,6442497,49623030,382873959,
%T A147961 2956927518,22848289569,176600866734,1365216845031,10554773538150,
%U A147961 81605126571777,630953992102374,4878478728359847,37720263000939822,291653357975402913,2255071616673820830,17436298586897553831
%N A147961 a(n) = ((6+sqrt(3))^n + (6-sqrt(3))^n)/2.
%H A147961 Harvey P. Dale, <a href="/A147961/b147961.txt">Table of n, a(n) for n = 0..1000</a>
%H A147961 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-33).
%F A147961 From _Philippe Deléham_, Nov 19 2008: (Start)
%F A147961 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1, with a(0)=1, a(1)=6.
%F A147961 G.f.: (1-6x)/(1-12x+33x^2).
%F A147961 a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2k)*3^(n-k))/6^n. (End)
%F A147961 E.g.f.: exp(6*x)*cosh(sqrt(3)*x). - _Stefano Spezia_, Apr 23 2025
%e A147961 a(3)=270
%t A147961 CoefficientList[Series[(1-6x)/(1-12x+33x^2),{x,0,30}],x] (* or *) LinearRecurrence[{12,-33},{1,6},30] (* _Harvey P. Dale_, Jul 30 2021 *)
%o A147961 (Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((6+r3)^n+(6-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 19 2008
%Y A147961 Cf. A098158.
%K A147961 nonn,easy
%O A147961 0,2
%A A147961 Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008
%E A147961 Extended beyond a(6) by _Klaus Brockhaus_, Nov 19 2008