A220745 "Complement" of Pol's E-toothpick sequence after n iterations.

0, 1, 4, 13, 28, 37, 64, 85, 112, 145, 172, 217, 256, 289, 364, 433, 508, 577, 628, 709, 748, 829, 904, 961, 1060, 1141, 1216, 1357, 1480, 1609, 1732, 1825, 1948, 2017, 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

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.

Links

Table of n, a(n) for n=0..59.

Formula

a(n)=3*n^2-A161330(n)

Crossrefs

Cf. A161330.

Sequence in context: A079430 A270942 A272455 * A298017 A356984 A307272

Adjacent sequences: A220742 A220743 A220744 * A220746 A220747 A220748

Keyword

nonn

Author

L. Edson Jeffery, Dec 21 2012

Status

approved