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 A244975 #41 Apr 02 2025 18:23:50
%S A244975 0,1,11,84,598,4199,29409,205882,1441196,10088397,70618807,494331680,
%T A244975 3460321794,24222252595,169555768205,1186890377478,8308232642392,
%U A244975 58157628496793,407103399477603,2849723796343276,19948066574402990,139636466020820991,977455262145747001
%N A244975 a(n) = (7^n - 2*n - 1)/4.
%C A244975 This formula is considered in Theorem 5 of Shum's paper in References: on page 4 reads M(7^m,3) = (7^m - 2*m - 1)/4 for m >= 1, where M(r,s) is the number of the codewords in an optimal CAC(r,s), and CAC(r,s) denotes a conflict-avoiding codes of length r and weight s (see Introduction).
%H A244975 Vincenzo Librandi, <a href="/A244975/b244975.txt">Table of n, a(n) for n = 0..1000</a>
%H A244975 K. W. Shum, <a href="http://dx.doi.org/10.1109/IWSDA.2011.6159407">On Conflict-Avoiding Codes of Weight Three and Odd Length</a>, The Fifth International Workshop on Signal Design and Its Applications in Communications, October 10-14, 2011, Guilin, China.
%H A244975 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F A244975 G.f.: x*(1+2*x)/((1-7*x)*(1-x)^2).
%F A244975 a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - _Robert Israel_, Jul 09 2014
%F A244975 From _Elmo R. Oliveira_, Apr 02 2025: (Start)
%F A244975 E.g.f.: exp(x)*(exp(6*x) - (2*x + 1))/4.
%F A244975 a(n) = (A000420(n) - A005408(n))/4. (End)
%t A244975 Table[(7^n - 2 n - 1)/4, {n, 0, 30}] (* or *)
%t A244975 CoefficientList[Series[x (1 + 2 x)/((1 - 7 x) (1 - x)^2), {x, 0, 30}], x]
%o A244975 (Magma) [(7^n-2*n-1)/4: n in [0..25]];
%Y A244975 Cf. A000420, A005408, A111277, A135304.
%K A244975 nonn,easy
%O A244975 0,3
%A A244975 _Vincenzo Librandi_, Jul 09 2014
%E A244975 Edited by _Bruno Berselli_, Jul 09 2014