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 A274074 #20 Mar 13 2025 11:07:17
%S A274074 2,5,37,215,1297,7775,46657,279935,1679617,10077695,60466177,
%T A274074 362797055,2176782337,13060694015,78364164097,470184984575,
%U A274074 2821109907457,16926659444735,101559956668417,609359740010495,3656158440062977,21936950640377855,131621703842267137
%N A274074 a(n) = 6^n+(-1)^n.
%H A274074 Michael De Vlieger, <a href="/A274074/b274074.txt">Table of n, a(n) for n = 0..1285</a>
%H A274074 Weerayuth Nilsrakoo and Achariya Nilsrakoo, <a href="https://doi.org/10.37394/23206.2025.24.7">On One-Parameter Generalization of Jacobsthal Numbers</a>, WSEAS Trans. Math. (2025) Vol. 24, 51-61. See p. 3.
%H A274074 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,6).
%F A274074 O.g.f.: (2-5*x) / ((1+x)*(1-6*x)).
%F A274074 E.g.f.: exp(-x) + exp(6*x).
%F A274074 a(n) = 5*a(n-1)+6*a(n-2) for n>1.
%t A274074 Array[6^# + (-1)^# &, 23, 0] (* or *)
%t A274074 LinearRecurrence[{5, 6}, {2, 5}, 23] (* or *)
%t A274074 CoefficientList[ Series[(5x -2)/(6x^2 + 5x -1), {x, 0, 23}], x] (* _Robert G. Wilson v_, Jan 01 2017 *)
%o A274074 (PARI) Vec((2-5*x)/((1+x)*(1-6*x)) + O(x^30))
%Y A274074 Sequences of the type k^n+(-1)^n: A014551 (k=2), A102345 (k=3), A201455 (k=4), A087404 (k=5), this sequence (k=6).
%K A274074 nonn,easy
%O A274074 0,1
%A A274074 _Colin Barker_, Jun 09 2016