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%I #6 Dec 21 2012 14:40:23
%S 0,1,4,13,28,37,64,85,112,145,172,217,256,289,364,433,508,577,628,709,
%T 748,829,904,961,1060,1141,1216,1357,1480,1609,1732,1825,1948,2017,
%U 2128,2245,2356,2509,2656,2797,2944,3097,3292,3481,3628,3817,3964,4117,4300,4489,4648,4849,5209,5416,5581,5788,5965,6196,6445,6700
%N "Complement" of Pol's E-toothpick sequence after n iterations.
%C In the E-toothpick pattern of Omar E. Pol (see A161330 and accompanying drawings), equivalently each E-toothpick can be replaced by a rhombus (with edge or side length = 1) in an obvious way. Let r denote the area of the rhombus. The n-th iteration of the pattern is bounded by a regular hexagon with edge length n, so the total area of that n-th hexagonal region is equal to 3*n^2*r. Then after n iterations, a(n) = (total area in the bounded hexagonal region not occupied by rhombi)/r = (number of "missing rhombi"). The resulting pattern of the unoccupied region we call the "complement" of the E-toothpick pattern.
%F a(n)=3*n^2-A161330(n)
%Y Cf. A161330.
%K nonn
%O 0,3
%A _L. Edson Jeffery_, Dec 21 2012
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