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%I #25 Dec 20 2013 18:18:23
%S 1,3,6,10,15,19,25,33,42,46,52,60,70,78,90,106,123,127,133,141,151,
%T 159,171,187,205,213,225,241,261,277,301,333,366,370,376,384,394,402,
%U 414,430,448,456,468,484,504,520,544,576,610,618,630,646,666,682
%N Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1.
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiGraph.html">Sierpinski Graph</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>
%F a(2^k) = A067771(k), k >= 0.
%e Illustration of initial terms:
%e -----------------------------------------------------
%e . Diagram n A233775(n) a(n)
%e -----------------------------------------------------
%e . * 0 1 1
%e . /T\
%e . *---* 1 2 3
%e . /T\ /T\
%e . *---*---* 2 3 6
%e . /T\ /T\
%e . *---* *---* 3 4 10
%e . /T\ /T\ /T\ /T\
%e . *---*---*---*---* 4 5 15
%e . /T\ /T\
%e . *---* *---* 5 4 19
%e .
%e After five stages the number of "black" triangles in the structure is A006046(5) = 11. The total number of vertices is 19, so a(5) = 19.
%Y Partial sums of A233775.
%Y Cf. A001316, A006046, A047999, A067771.
%K nonn
%O 0,2
%A _Omar E. Pol_, Dec 16 2013
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