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 A319611 #7 Nov 09 2018 21:06:10
%S A319611 0,0,1,1,2,2,3,2,3,4,5,5,6,6,7,6,6,7,9,8,8,10,13,11,10,11,14,15,13,14,
%T A319611 16,13,14,16,19,17,17,17,20,20,16,18,20,19,22,21,22,21,22,20,26,29,25,
%U A319611 26,28,28,27,27,32,30,29,30,35,31,27,28,32,32,32,34,37,30,27,36,37,39,42,41,43,41,34
%N A319611 a(n) is the number of gaps in the n-th generation of the rule-30 1D cellular automaton started from a single ON.
%C A319611 OFF cells outside the triangle of active cells are ignored.
%e A319611 The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle:
%e A319611 1 . a(1)= (0)
%e A319611 2 . . . a(2)= (0)
%e A319611 3 . . 0 0 . a(3)= (1)
%e A319611 4 . . 0 . . . . a(4)= (1)
%e A319611 5 . . 0 0 . 0 0 0 . a(5)= (2)
%e A319611 6 . . 0 . . . . 0 . . . a(6)= (2)
%e A319611 7 . . 0 0 . 0 0 0 0 . 0 0 . a(7)= (3)
%e A319611 8 . . 0 . . . . 0 0 . . . . . . a(8)= (2)
%e A319611 9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 . a(9)= (3)
%e A319611 10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . . a(10)=(4)
%e A319611 11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 . a(11)=(5)
%e A319611 12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . . a(12)=(5)
%e A319611 13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 . a(13)=(6)
%t A319611 CellularAutomaton[30, {{1}, 0}, 200];
%t A319611 (Reverse[Internal`DeleteTrailingZeros[
%t A319611 Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
%t A319611 Table[
%t A319611 Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Length,
%t A319611 {i, 1, % // Length}
%t A319611 ]
%Y A319611 Cf. A100053.
%K A319611 nonn
%O A319611 0,5
%A A319611 _Philipp O. Tsvetkov_, Sep 24 2018