ConwayLife.com

It appears that the number of hearts present in the n-th generation (Sloane's A188346) equals the number of rectangles of area = 2 present in the (n - 2)nd generation of the toothpick structure of Sloane's A139250, assuming the toothpicks have length 2, if n >= 3.

Note that every object is a closed region which contains 2^k virtual circles with radius 1 and 2^k-1 virtual diamonds, for example: a 2x2-object is a closed region which contains exactly four virtual circles and three virtual diamonds, a 2x4-object is a closed region which contains exactly 8 virtual ...