OFFSET
0,1
COMMENTS
Also the binary expansion of the constant 5/17 = 2^(-2) + 2^(-5) + 2^(-7) + ... - R. J. Mathar, Mar 27 2009
Period 8: repeat [0, 1, 0, 0, 1, 0, 1, 1]. - Wesley Ivan Hurt, Aug 23 2015
LINKS
Wikipedia, Paradiddle
Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).
FORMULA
From R. J. Mathar, Mar 27 2009: (Start)
a(n) = a(n-8) = a(n-1) - a(n-4) + a(n-5).
G.f.: -x*(1+x^3-x)/((x-1)*(1+x^4)). (End)
a(n) = (1-(-1)^((n+5)*(n+6)*(n^2+11*n+32)/8))/2. - Wesley Ivan Hurt, Aug 23 2015
a(n) = A165211(n+5). - Wesley Ivan Hurt, Aug 23 2015
MAPLE
A130198:= n -> [0, 1, 0, 0, 1, 0, 1, 1][(n mod 8)+1]: seq(A130198(n), n=0..100); # Wesley Ivan Hurt, Aug 23 2015
MATHEMATICA
CoefficientList[Series[x*(1 - x + x^3)/((1 - x)*(1 + x^4)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 23 2015 *)
PROG
(PARI) a(n)=((n%8>3)+(n%4==1))%2 \\ Jaume Oliver Lafont, Mar 19 2009
(PARI) a(n)=210\2^(n%8)%2; \\ Jaume Oliver Lafont, Mar 24 2009
(PARI) apply( A130198(n)=bittest(210, n%8), [0..99]) \\ M. F. Hasler, May 24 2019
(Magma) [(1-(-1)^((n+5)*(n+6)*(n^2+11*n+32) div 8))/2 : n in [0..100]]; // Wesley Ivan Hurt, Aug 23 2015
(Python)
def A130198(n): return n&1^bool(n+1&4) # Chai Wah Wu, Aug 30 2024
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Simone Severini, May 16 2007
STATUS
approved