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 A016170 #31 Nov 11 2024 03:43:48
%S A016170 1,14,148,1400,12496,107744,908608,7548800,62070016,506637824,
%T A016170 4113568768,33271347200,268347559936,2159841173504,17357093552128,
%U A016170 139326933401600,1117436577120256,8956419276406784,71752914167922688
%N A016170 Expansion of 1/((1-6*x)*(1-8*x)).
%H A016170 G. C. Greubel, <a href="/A016170/b016170.txt">Table of n, a(n) for n = 0..1000</a>
%H A016170 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-48).
%F A016170 a(n) = Sum_{k=1..n} 2^(n-1)*3^(n-k)*binomial(n,k). - _Zerinvary Lajos_, Sep 24 2006
%F A016170 From _R. J. Mathar_, Sep 18 2008: (Start)
%F A016170 a(n) = 4*8^n - 3*6^n = A081201(n+1).
%F A016170 Binomial transform of A081033. (End)
%F A016170 a(n) = 8*a(n-1) + 6^n. - _Vincenzo Librandi_, Feb 09 2011
%F A016170 a(0)=1, a(1)=14, a(n) = 14*a(n-1) - 48*a(n-2). - _Harvey P. Dale_, Dec 08 2011
%F A016170 E.g.f.: 4*exp(8*x) - 3*exp(6*x). - _G. C. Greubel_, Nov 10 2024
%p A016170 A016170:=n->4*8^n-3*6^n: seq(A016170(n), n=0..30); # _Wesley Ivan Hurt_, May 03 2017
%t A016170 CoefficientList[Series[1/((1-6x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-48},{1,14},30] (* _Harvey P. Dale_, Dec 08 2011 *)
%o A016170 (PARI) Vec(1/((1-6*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%o A016170 (Magma) [n le 2 select 14^(n-1) else 14*Self(n-1) -48*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 10 2024
%o A016170 (SageMath)
%o A016170 A016170=BinaryRecurrenceSequence(14,-48,1,14)
%o A016170 [A016170(n) for n in range(31)] # _G. C. Greubel_, Nov 10 2024
%Y A016170 Cf. A081033, A081201, A016129.
%K A016170 nonn,easy
%O A016170 0,2
%A A016170 _N. J. A. Sloane_