OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.
Wikipedia, Sierpinski triangle.
FORMULA
a(2^k) = A067771(k), k >= 0.
EXAMPLE
Illustration of initial terms:
-----------------------------------------------------
Diagram n A233775(n) a(n)
-----------------------------------------------------
* 0 1 1
/T\
*---* 1 2 3
/T\ /T\
*---*---* 2 3 6
/T\ /T\
*---* *---* 3 4 10
/T\ /T\ /T\ /T\
*---*---*---*---* 4 5 15
/T\ /T\
*---* *---* 5 4 19
-----------------------------------------------------
After five stages the number of "black" triangles in the structure is A006046(5) = 11. The total number of vertices is 19, so a(5) = 19.
MATHEMATICA
A233775[n_] := If[n == 0, 1, (2^IntegerExponent[n, 2]+1)*2^(DigitSum[n, 2]-1)];
Accumulate[Array[A233775, 100, 0]] (* Paolo Xausa, Aug 07 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 16 2013
STATUS
approved