OFFSET
0,2
COMMENTS
Robert Fathauer observed that if the "warp and woof" construction used by Jim Conant in his recursive dissection of a square (see A328078) is applied to a triangle, one obtains the Sierpinski gasket.
The present sequence gives the number of regions after the n-th generation of this dissection of a triangle.
REFERENCES
Robert Fathauer, Email to N. J. A. Sloane, Oct 14 2019.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3).
FORMULA
From Colin Barker, Nov 27 2019: (Start)
G.f.: (1 + x + x^2 - 2*x^3) / ((1 - x)*(1 - 3*x^3)).
a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) for n>3.
(End)
MAPLE
f:=proc(n) option remember;
if n<=2 then n+1 else 3*f(n-3)+1; fi; end;
[seq(f(n), n=0..50)];
PROG
(PARI) Vec((1 + x + x^2 - 2*x^3) / ((1 - x)*(1 - 3*x^3)) + O(x^40)) \\ Colin Barker, Nov 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 27 2019
STATUS
approved