The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #20 Mar 30 2012 17:34:05
%S 0,1,3,6,9,12,15,19,24,30,36,42,48,55,63,72,81,90,99,109,120,132,144,
%T 156,168,181,195,210,225,240,255,271,288,306,324,342,360,379,399,420,
%U 441,462,483,505,528,552,576,600,624,649,675,702,729,756,783,811
%N Concentric triangular numbers (see Comments lines for definition).
%C 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 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 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F 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 Using the numbers A008486 we can write:
%e 0, 1, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,...
%e 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 9, 12, 15, 18,...
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,...
%e And so on.
%e =========================================================
%e The sums of the columns give this sequence:
%e 0, 1, 3, 6, 9, 12, 15, 19, 24, 30, 36, 42, 48, 55,...
%e ...
%e Illustration of initial terms:
%e . o
%e . o o o
%e . o o o o o
%e . o o o o o o o
%e . o o o o o o o o o
%e . o o o o o o o o o o o o o o o o o o o o o
%e .
%e . 1 3 6 9 12 15
%e .
%e . o
%e . o o o
%e . o o o o o
%e . o o o o o o
%e . o o o o o o o
%e . o o o o o o o o o
%e . o o o o o o o o o o o o
%e . o o o o o o
%e . 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 .
%e . 19 24 30
%Y Cf. A000217, A008486, A032528, A069131, A152751, A194272, A194274, A194275.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Aug 20 2011