|
%I #22 May 14 2021 19:38:45
%S 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 92,100,108,116,125,135,145,155,165,175,186,198,210,222,234,246,259,
%U 273,287,301,315,329,344,360,376,392,408,424,441
%N 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 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 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 Kival Ngaokrajang, <a href="/A268292/a268292.pdf">Illustration of initial terms</a>, <a href="/A268292/a268292_1.pdf">Continuously concatenate pattern</a>
%F Empirical g.f.: x^7 / ((1-x)^3*(1-x+x^2)*(1+x+x^2)). - _Colin Barker_, Jan 31 2016
%o (PARI) a = 3; d1 = 2; print1("0, 0, 0, 0, 0, 0, 0, 1, 3, ");
%o 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 Cf. A112421, A267489, A014682.
%K base,nonn
%O 0,9
%A _Kival Ngaokrajang_, Jan 31 2016
|
