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 A378497 #35 Mar 31 2025 01:47:26
%S A378497 1,6,24,99,398,1592,6371,25486,101944,407779,1631118,6524472,26097891,
%T A378497 104391566,417566264,1670265059,6681060238,26724240952,106896963811,
%U A378497 427587855246,1710351420984,6841405683939,27365622735758,109462490943032,437849963772131
%N A378497 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 2,0,3.
%H A378497 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).
%F A378497 a(n) = floor((7/18)*4^n).
%F A378497 G.f.: z*(2*z^3+2*z+1)/((z-1)*(4*z-1)*(z^2+z+1)).
%F A378497 E.g.f.: (9 - 10*exp(x) + 7*exp(4*x) - 2*exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)))/18. - _Stefano Spezia_, Nov 29 2024
%e A378497 a(7) = 1203203_4 = 6371.
%e A378497 a(8) = 12032032_4 = 25486.
%t A378497 Table[FromDigits[Join[{1},PadRight[{}, n-1, {2, 0, 3}]], 4], {n, 30}]
%Y A378497 Cf. A378499, A037667, A037618, A378502. Periodic part of sequence rotated right relative to A378499. Same first four terms as A037688, and similar formula.
%K A378497 nonn,base,easy
%O A378497 1,2
%A A378497 _Jonathan Shadrach Gilbert_, Nov 28 2024