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 A194273 #20 Mar 30 2012 17:34:05 %S A194273 0,1,3,6,9,12,15,19,24,30,36,42,48,55,63,72,81,90,99,109,120,132,144, %T A194273 156,168,181,195,210,225,240,255,271,288,306,324,342,360,379,399,420, %U A194273 441,462,483,505,528,552,576,600,624,649,675,702,729,756,783,811 %N A194273 Concentric triangular numbers (see Comments lines for definition). %C A194273 This can be interpreted as a cellular automaton on the infinite hexagonal net. The sequence gives the number of cells "ON" in the structure after n-th stage. A194272 gives the first differences. For a definition without words see the illustration of initial terms in the example section. For other concentric polygonal numbers see A194274, A194275 and A032528. %C A194273 Also, row sums of an infinite square array T(n,k) in which column k lists 6*k-1 zeros followed by the numbers A008486 (see example). %H A194273 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a> %F A194273 G.f.: x/(1-3*x+3*x^2-3*x^4+3*x^5-x^6) = x/((1-x)^3*(1+x)*(1-x+x^2)). %e A194273 Using the numbers A008486 we can write: %e A194273 0, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,... %e A194273 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 9, 12, 15, 18,... %e A194273 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,... %e A194273 And so on. %e A194273 ========================================================= %e A194273 The sums of the columns give this sequence: %e A194273 0, 1, 3, 6, 9, 12, 15, 19, 24, 30, 36, 42, 48, 55,... %e A194273 ... %e A194273 Illustration of initial terms: %e A194273 . o %e A194273 . o o o %e A194273 . o o o o o %e A194273 . o o o o o o o %e A194273 . o o o o o o o o o %e A194273 . o o o o o o o o o o o o o o o o o o o o o %e A194273 . %e A194273 . 1 3 6 9 12 15 %e A194273 . %e A194273 . o %e A194273 . o o o %e A194273 . o o o o o %e A194273 . o o o o o o %e A194273 . o o o o o o o %e A194273 . o o o o o o o o o %e A194273 . o o o o o o o o o o o o %e A194273 . o o o o o o %e A194273 . o o o o o o o o o o o o o o o o o o o o o o o o %e A194273 . %e A194273 . 19 24 30 %Y A194273 Cf. A000217, A008486, A032528, A069131, A152751, A194272, A194274, A194275. %K A194273 nonn,easy %O A194273 0,3 %A A194273 _Omar E. Pol_, Aug 20 2011