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 A370627 #40 Jul 22 2024 14:34:03
%S A370627 1,5,18,76,296,1200,4768,19136,76416,305920,1223168,4893696,19572736,
%T A370627 78295040,313171968,1252704256,5010784256,20043202560,80172679168,
%U A370627 320690978816,1282763390976,5131054612480,20524216352768,82096869605376,328387470032896,1313549896908800,5254199554080768
%N A370627 a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3 = 2^(n - 1)*A062092(n).
%H A370627 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,8).
%F A370627 Binomial transform of A133125.
%F A370627 G.f.: (1 + 3*x)/(1 - 2*x - 8*x^2).
%F A370627 E.g.f.: (1/3)*exp(x)*(3*exp(3*x) + sinh(3*x)).
%F A370627 a(n) = 2*a(n-1) + 8*a(n-2), for n > 1.
%F A370627 a(n) = 4*a(n-1) + (-2)^n, for n > 0.
%F A370627 a(n) = (a(n+2) - 2*a(n+1))/8.
%F A370627 From _Thomas Scheuerle_, Jul 03 2024: (Start)
%F A370627 a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3.
%F A370627 a(n) = A003683(n) + 4^n.
%F A370627 a(n) = A255470(2^n - 1) - A255470(2^(n-1) - 1) = A255471(n) - A255471(n-1), for n > 0. (End)
%F A370627 Binomial transform: A108982.
%t A370627 LinearRecurrence[{2, 8}, {1, 5}, 27] (* _Amiram Eldar_, Jul 03 2024 *)
%o A370627 (PARI) a(n) = 2^(n-1)*((-1)^(n+1) + 7*2^n)/3 \\ _Thomas Scheuerle_, Jul 03 2024
%Y A370627 Cf. A003683, A122803, A133125, A255470, A255471.
%Y A370627 Cf. A108982, A062092.
%K A370627 nonn,easy
%O A370627 0,2
%A A370627 _Paul Curtz_, Jul 03 2024