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 A081336 #34 May 06 2025 11:20:09
%S A081336 1,5,29,185,1241,8525,59189,412865,2885681,20186645,141267149,
%T A081336 988751945,6920909321,48445302365,339113927909,2373787929425,
%U A081336 16616486808161,116315321563685,814206992665469,5699448173817305,39896134892198201
%N A081336 a(n) = (7^n + 3^n)/2.
%C A081336 Binomial transform of A081336.
%C A081336 5th binomial transform of (1,0,4,0,16,0,64,...).
%H A081336 Vincenzo Librandi, <a href="/A081336/b081336.txt">Table of n, a(n) for n = 0..200</a>
%H A081336 Yassine Otmani, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Otmani/otmani10.html">The 2-Pascal Triangle and a Related Riordan Array</a>, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 12.
%H A081336 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-21).
%F A081336 a(n) = 10*a(n-1) - 21*a(n-2), a(0)=1, a(1)=5.
%F A081336 G.f.: (1-5*x)/((1-3*x)*(1-7*x)).
%F A081336 E.g.f.: exp(5*x) * cosh(2*x).
%F A081336 a(n) = A074608(n) / 2. - _Michel Marcus_, Oct 07 2015
%F A081336 a(n) = Sum_{k=0..n} A027907(n,2k)*4^k . - _J. Conrad_, Aug 24 2016
%t A081336 CoefficientList[Series[(1 - 5 x) / ((1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%t A081336 LinearRecurrence[{10,-21},{1,5},30] (* _Harvey P. Dale_, Dec 07 2014 *)
%o A081336 (Magma) [(7^n+3^n)/2: n in [0..25]]; // _Vincenzo Librandi_, Aug 08 2013
%o A081336 (PARI) a(n)=(7^n+3^n)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A081336 Cf. A074608, A081337.
%K A081336 nonn,easy
%O A081336 0,2
%A A081336 _Paul Barry_, Mar 18 2003