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 A154348 #29 Sep 08 2022 08:45:40
%S A154348 1,16,200,2304,25664,281600,3068416,33325056,361369600,3915710464,
%T A154348 42414669824,459354931200,4974457389056,53867442077696,
%U A154348 583309459456000,6316374594945024,68396663789584384,740629643316428800
%N A154348 a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=1, a(1)=16.
%C A154348 Third binomial transform of A164609, fourth binomial transform of A164608, fifth binomial transform of A054490, sixth binomial transform of A164607, seventh binomial transform of A083100, eighth binomial transform of A164683.
%C A154348 lim_{n -> infinity} a(n)/a(n-1) = 8 + 2*sqrt(2) = 10.8284271247....
%H A154348 R. J. Mathar, <a href="/A154348/b154348.txt">Table of n, a(n) for n = 0..100</a>
%H A154348 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-56).
%F A154348 a(n) = 16*a(n-1) - 56*a(n-2) for n>1. - _Philippe Deléham_, Jan 12 2009
%F A154348 a(n) = ( (8 + 2*sqrt(2))^n - (8 - 2*sqrt(2))^n )/(4*sqrt(2)).
%F A154348 G.f.: 1/(1 - 16*x + 56*x^2). - _Klaus Brockhaus_, Jan 12 2009; corrected Oct 08 2009
%F A154348 E.g.f.: (1/(2*sqrt(2)))*exp(8*x)*sinh(2*sqrt(2)*x). - _G. C. Greubel_, Sep 13 2016
%t A154348 Join[{a=1,b=16},Table[c=16*b-56*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011*)
%t A154348 LinearRecurrence[{16,-56},{1,16},30] (* _Harvey P. Dale_, Aug 31 2016 *)
%o A154348 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((8+2*r)^n-(8-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jan 12 2009
%Y A154348 Cf. A002193 (decimal expansion of sqrt(2)), A164609, A164608, A054490, A164607, A083100, A164683.
%K A154348 nonn,easy
%O A154348 0,2
%A A154348 Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
%E A154348 Extended beyond a(7) by _Klaus Brockhaus_, Jan 12 2009
%E A154348 Edited by _Klaus Brockhaus_, Oct 08 2009
%E A154348 Offset corrected. - _R. J. Mathar_, Jun 19 2021