OFFSET
1,3
COMMENTS
Stanica observes that the sequence in binary forms a pattern where 1 bits are inserted into the word 1010101...:
1 11
101 1011 1101
10101 101011 101101 110101
1010101 10101011 10101101 10110101 11010101...
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..5050
P. Stanica, p^q Catalan numbers and squarefree binomial coefficients, arXiv:math/0010148 [math.NT], 2000.
MATHEMATICA
Select[ Range[0, 65000], Mod[ Binomial[4#, # ]/(3# + 1), 4] != 0 &] (* Robert G. Wilson v, Oct 12 2005 *)
PROG
(PARI) isok(n) = binomial(4*n, n)/(3*n+1) % 4; \\ Michel Marcus, Apr 16 2015
(Magma) [n: n in [0..2*10^4] | not IsZero(Binomial(4*n, n) div (3*n+1) mod 4)]; // Vincenzo Librandi, Apr 16 2015
(Python)
from __future__ import division
A078971_list = []
for t in range(100):
A078971_list.append((2**(2*t)-1)//3)
for j in range(t):
A078971_list.append((2**(2*t+1)+2**(2*j+1)-1)//3) # Chai Wah Wu, Mar 06 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 14 2003
EXTENSIONS
Comments and more terms from Ralf Stephan, Oct 30 2003
a(28)-a(44) from Robert G. Wilson v, Oct 12 2005
STATUS
approved