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 A378499 #24 Dec 21 2024 00:19:48
%S A378499 1,4,19,78,312,1251,5006,20024,80099,320398,1281592,5126371,20505486,
%T A378499 82021944,328087779,1312351118,5249404472,20997617891,83990471566,
%U A378499 335961886264,1343847545059,5375390180238,21501560720952,86006242883811,344024971535246
%N A378499 a(n) is the number whose base-4 digits are 1 followed by the first n-1 terms of the periodic sequence with initial period 0,3,2.
%H A378499 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).
%F A378499 a(n) = floor((11/36)*4^n).
%F A378499 G.f.: z*(z^3+3*z^2+1)/((z-1)*(4*z-1)*(z^2+z+1)).
%F A378499 E.g.f.: (9 - 20*exp(x) + 11*exp(4*x) + 8*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2))/36. - _Stefano Spezia_, Nov 29 2024
%e A378499 a(7) = 1032032_4 = 5006.
%e A378499 a(8) = 10320320_4 = 20024.
%t A378499 Table[FromDigits[Join[{1}, PadRight[{}, n-1, {0, 3, 2}]], 4], {n, 30}]
%Y A378499 Cf.: A378497, A037667, A037618, A037681, A378502. Periodic part of sequence rotated left relative to A378497.
%K A378499 nonn,base,easy
%O A378499 1,2
%A A378499 _Jonathan Shadrach Gilbert_, Nov 28 2024