OFFSET
0,3
COMMENTS
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.
FORMULA
a(n)=3*n^2-A161330(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
L. Edson Jeffery, Dec 21 2012
STATUS
approved