OFFSET
0,3
COMMENTS
All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.
Similar to A271061. - Robert Price, Mar 30 2016
For n=3,5,..., also the number of minimum vertex colorings in the n-sunlet graph. - Eric W. Weisstein, Mar 03 2024
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Eric Weisstein's World of Mathematics, Minimum Vertex Coloring.
Eric Weisstein's World of Mathematics, Sunlet Graph.
Index entries for linear recurrences with constant coefficients, signature (6,-8).
FORMULA
G.f.: 8*x^2 / ((1-2*x)*(1-4*x)). - Colin Barker, Mar 30 2016
a(n) = 6*a(n-1)-8*a(n-2) for n>2. - Colin Barker, Mar 30 2016
EXAMPLE
For n = 3 the area of all squares and rectangles in the toothpick structure after 2^3 stages equals the area of a rectangle of size 8X6, so a(3) = 8*6 = 48.
PROG
(PARI) concat(vector(2), Vec(8*x^2/((1-2*x)*(1-4*x)) + O(x^50))) \\ Colin Barker, Mar 30 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 21 2012
STATUS
approved