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 A084136 #17 Oct 13 2022 17:32:52
%S A084136 1,1,5,13,57,201,797,2997,11569,44113,169205,647197,2478825,9488025,
%T A084136 36327821,139071813,532438369,2038379425,7803827429,29876310829,
%U A084136 114379413657,437893003113,1676441901821,6418134825429,24571362963601
%N A084136 Binomial transform of cosh(sqrt(2)*x)^2.
%H A084136 G. C. Greubel, <a href="/A084136/b084136.txt">Table of n, a(n) for n = 0..1000</a>
%H A084136 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,-7).
%F A084136 a(n) = ((1+sqrt(8))^n + (1-sqrt(8))^n + 2)/4.
%F A084136 a(n) = (A084058(n) + 1)/2.
%F A084136 E.g.f.: exp(x)*cosh(sqrt(2)*x)^2.
%F A084136 G.f.: (1+x)*(1-3*x) / ( (1-x)*(1-2*x-7*x^2) ). - _R. J. Mathar_, Nov 09 2012
%t A084136 LinearRecurrence[{3,5,-7},{1,1,5},30] (* _Harvey P. Dale_, Nov 08 2017 *)
%o A084136 (PARI) my(x='x+O('x^30)); round(Vec(serlaplace(exp(x)*cosh(sqrt(2)*x)^2))) \\ _G. C. Greubel_, Sep 11 2018
%o A084136 (Magma) I:=[1,1,5]; [n le 3 select I[n] else 3*Self(n-1) +5*Self(n-2) - 7*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Sep 11 2018
%o A084136 (SageMath)
%o A084136 A084058=BinaryRecurrenceSequence(2,7,1,1)
%o A084136 def A084136(n): return (1+A084058(n))/2
%o A084136 [A084136(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%Y A084136 Cf. A084058, A084137.
%K A084136 easy,nonn
%O A084136 0,3
%A A084136 _Paul Barry_, May 16 2003