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 A154347 #16 Sep 08 2022 08:45:40
%S A154347 1,14,155,1596,15989,158410,1562191,15375864,151212265,1486561286,
%T A154347 14612155139,143621159220,1411597868381,13873902629314,
%U A154347 136359124206775,1340197731092976,13172044142823889,129460511024722430
%N A154347 a(n) = ( (7 + 2*sqrt(2))^n - (7 - 2*sqrt(2))^n )/(4*sqrt(2)).
%C A154347 Fourth binomial transform of A054489.
%C A154347 lim_{n -> infinity} a(n)/a(n-1) = 7 + 2*sqrt(2) = 9.8284271247....
%H A154347 G. C. Greubel, <a href="/A154347/b154347.txt">Table of n, a(n) for n = 1..1000</a>
%H A154347 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-41).
%F A154347 a(n) = 14*a(n-1) - 41*a(n-2) for n>1, with a(0)=0, a(1)=1. - _Philippe Deléham_, Jan 12 2009
%F A154347 G.f.: x/(1 - 14*x + 41*x^2). - _Klaus Brockhaus_, Jan 12 2009, corrected Oct 08 2009
%F A154347 E.g.f.: (1/4*sqrt(2))*exp(7*x)*sinh(2*sqrt(2)*x). - _G. C. Greubel_, Sep 13 2016
%p A154347 A154347:=n->((7+2*sqrt(2))^n-(7-2*sqrt(2))^n)/(4*sqrt(2)): seq(simplify(A154347(n)), n=1..30); # _Wesley Ivan Hurt_, Sep 13 2016
%t A154347 LinearRecurrence[{14,-41},{1,14}, 25] (* or *) Table[( (7 + 2*sqrt(2))^n - (7 - 2*sqrt(2))^n )/(4*sqrt(2)),{n,1,25}] (* _G. C. Greubel_, Sep 13 2016 *)
%o A154347 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((7+2*r)^n-(7-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jan 12 2009
%Y A154347 Cf. A002193 (decimal expansion of sqrt(2)), A054489.
%K A154347 nonn
%O A154347 1,2
%A A154347 Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
%E A154347 Extended beyond a(7) by _Klaus Brockhaus_, Jan 12 2009
%E A154347 Edited by _Klaus Brockhaus_, Oct 08 2009