login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060547 a(n) = 2^(floor(n/3) + ((n mod 3) mod 2)). 7
2, 1, 2, 4, 2, 4, 8, 4, 8, 16, 8, 16, 32, 16, 32, 64, 32, 64, 128, 64, 128, 256, 128, 256, 512, 256, 512, 1024, 512, 1024, 2048, 1024, 2048, 4096, 2048, 4096, 8192, 4096, 8192, 16384, 8192, 16384, 32768, 16384, 32768, 65536, 32768, 65536, 131072 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) is the number of patterns, invariant under 120-degree rotations, that may appear in a top-down equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement.
The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.
LINKS
FORMULA
a(n) = 2^A008611(n-1) for n >= 1.
Sum_{n>=1} 1/a(n) = 4. - Amiram Eldar, Dec 10 2022
MAPLE
gf := (1+x^2+x^4)/(1-x^3)^2: s := series(gf, x, 100):
for i from 0 to 70 do printf(`%d, `, 2^coeff(s, x, i)) od:
# Alternative:
a := n -> 2^(iquo(n, 3) + irem(irem(n, 3), 2));
seq(a(n), n = 1..49); # Peter Luschny, Nov 26 2022
MATHEMATICA
CoefficientList[ Series[ (2x^2+x+2) / (1-2x^3), {x, 0, 48}], x] (* Jean-François Alcover, Nov 18 2011 *)
PROG
(PARI) { for (n=1, 500, write("b060547.txt", n, " ", 2^(floor(n/3) + (n % 3) % 2)); ) } \\ Harry J. Smith, Jul 07 2009
(Haskell)
a060547 = (2 ^) . a008611 . (subtract 1)
a060547_list = f [2, 1, 2] where f xs = xs ++ f (map (* 2) xs)
-- Reinhard Zumkeller, Nov 25 2013
def a_gen():
a, b, c = 1, 2, 4
yield b
while True:
yield a
a, b, c = b, c, a + a
a = a_gen()
print([next(a) for _ in range(51)]) # Peter Luschny, Nov 26 2022
CROSSREFS
Sequence in context: A307018 A274624 A263050 * A079878 A324469 A329688
KEYWORD
easy,nice,nonn
AUTHOR
André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
EXTENSIONS
More terms from James A. Sellers, Apr 04 2001
Name replaced with given formula by Peter Luschny, Nov 26 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)