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 A268292 #25 Jun 02 2025 14:44:44
%S A268292 0,0,0,0,0,0,0,1,3,5,7,9,11,14,18,22,26,30,34,39,45,51,57,63,69,76,84,
%T A268292 92,100,108,116,125,135,145,155,165,175,186,198,210,222,234,246,259,
%U A268292 273,287,301,315,329,344,360,376,392,408,424,441
%N A268292 a(n) is the total number of isolated 1's at the boundary between n-th and (n-1)-th iterations in the pattern of A267489.
%C A268292 Refer to pattern of A267489, The total number of isolated 1's is a(n) and A112421 when consider at the boundary between n-th and (n-1)-th iterations and at the boundary in the same iterations concatenate on horizontal respectively. See illustrations in the links.
%C A268292 Empirically, a(n+4) gives the number of solutions m where 0 < m < 2^n and A014682^n(m) < 3 and A014682^n(m+2^n) = A014682^n(m)+9. - _Thomas Scheuerle_, Apr 25 2021
%H A268292 Kival Ngaokrajang, <a href="/A268292/a268292.pdf">Illustration of initial terms</a>, <a href="/A268292/a268292_1.pdf">Continuously concatenate pattern</a>
%F A268292 Empirical g.f.: x^7 / ((1-x)^3*(1-x+x^2)*(1+x+x^2)). - _Colin Barker_, Jan 31 2016
%F A268292 For n>0: a(n) = floor((n-3)^2/12) + floor((n-4)^2/12). - _Hoang Xuan Thanh_, Jun 02 2025
%o A268292 (PARI) a = 3; d1 = 2; print1("0, 0, 0, 0, 0, 0, 0, 1, 3, ");
%o A268292 for (n = 3,100, d2 = 0; if (Mod(n,6)==1 || Mod(n,6)==2, d2 = 1); d1 = d1 + d2; a = a + d1; print1(a, ", "))
%Y A268292 Cf. A112421, A267489, A014682.
%K A268292 base,nonn
%O A268292 0,9
%A A268292 _Kival Ngaokrajang_, Jan 31 2016