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 A176281 #20 Feb 23 2025 12:41:27
%S A176281 1,3,12,56,280,1440,7488,39104,204544,1070592,5604864,29345792,
%T A176281 153653248,804532224,4212572160,22057287680,115493404672,604731211776,
%U A176281 3166413520896,16579556016128,86811681488896,454551863820288
%N A176281 Hankel transform of A176280.
%H A176281 G. C. Greubel, <a href="/A176281/b176281.txt">Table of n, a(n) for n = 0..1000</a>
%H A176281 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16,8).
%F A176281 G.f.: (1-5*x+4*x^2)/(1-8*x+16*x^2-8*x^3) = (1-5*x+4*x^2)/((1-2*x)*(1-6*x+4*x^2)).
%F A176281 a(n) = 2^(n-1) + (3-sqrt(5))^n*((5-sqrt(5))/20) + (3+sqrt(5))^n*((5+sqrt(5))/20).
%F A176281 a(n) = 2^(n-1) + A082761(n)/2. - _R. J. Mathar_, Sep 30 2012
%F A176281 a(0)=1, a(1)=3, a(2)=12, a(n) = 8*a(n-1) - 16*a(n-2) + 8*a(n-3). - _Harvey P. Dale_, Aug 14 2013
%F A176281 a(n) = 2^(n-1)*(Fibonacci(2*n+1) + 1). - _G. C. Greubel_, Nov 24 2019
%p A176281 with(combinat); seq(2^(n-1)*(fibonacci(2*n+1) + 1), n=0..30); # _G. C. Greubel_, Nov 24 2019
%t A176281 CoefficientList[Series[(1-5x+4x^2)/((1-2x)(1-6x+4x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{8,-16,8},{1,3,12},40] (* _Harvey P. Dale_, Aug 14 2013 *)
%o A176281 (PARI) vector(31, n, 2^(n-2)*(fibonacci(2*n-1) + 1)) \\ _G. C. Greubel_, Nov 24 2019
%o A176281 (Magma) [2^(n-1)*(Fibonacci(2*n+1) + 1): n in [0..30]]; // _G. C. Greubel_, Nov 24 2019
%o A176281 (Sage) [2^(n-1)*(fibonacci(2*n+1) + 1) for n in (0..30)] # _G. C. Greubel_, Nov 24 2019
%o A176281 (GAP) List([0..30], n-> 2^(n-1)*(Fibonacci(2*n+1) + 1)); # _G. C. Greubel_, Nov 24 2019
%Y A176281 Cf. A000045, A082761, A176280.
%K A176281 easy,nonn
%O A176281 0,2
%A A176281 _Paul Barry_, Apr 14 2010