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A003815 a(0) = 0, a(n) = a(n-1) XOR n. 7
0, 1, 3, 0, 4, 1, 7, 0, 8, 1, 11, 0, 12, 1, 15, 0, 16, 1, 19, 0, 20, 1, 23, 0, 24, 1, 27, 0, 28, 1, 31, 0, 32, 1, 35, 0, 36, 1, 39, 0, 40, 1, 43, 0, 44, 1, 47, 0, 48, 1, 51, 0, 52, 1, 55, 0, 56, 1, 59, 0, 60, 1, 63, 0, 64, 1, 67, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = ABS(A077140(n)) for n>0. - Reinhard Zumkeller, Oct 09 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = n+(-1)^n*a(n-1). - Vladeta Jovovic, Mar 13 2003

a(0)=0, a(4n+1)=1, a(4n+2)=4n+3, a(4n+3)=0, a(4n+4)=4n+4, n>=0.

a(n) = f(n,0) with f(n,x) = if n=0 then x else if x is even then f(n-1,x+n) else f(n-1,x-n). - Reinhard Zumkeller, Oct 09 2007

G.f.: x*(1+3*x-x^2+x^3)/((1-x^4)*(1-x^2)). - Vincenzo Librandi, Oct 12 2013 *)

MAPLE

(1+3*x-x^2+x^3)*x/(1-x^4)/(1-x^2);

MATHEMATICA

an = 0; Reap[ For[i = 0, i <= 100, i++, an = BitXor[an, i]; Sow[an]]][[2, 1]] (* Jean-Fran├žois Alcover, Oct 11 2013, translated fom Pari *)

CoefficientList[Series[x (1 + 3 x - x^2 + x^3)/((1 - x^4) (1 - x^2)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 12 2013 *)

PROG

(PARI) print1(an=0); for( i=1, 100, print1(", ", an=bitxor(an, i))) \\ M. F. Hasler, Oct 20 2008

CROSSREFS

Cf. A003816.

Cf. A077140 ; A145768. [From M. F. Hasler, Oct 20 2008]

Sequence in context: A195084 A138376 A077140 * A131486 A127445 A081170

Adjacent sequences:  A003812 A003813 A003814 * A003816 A003817 A003818

KEYWORD

nonn,base

AUTHOR

Marc LeBrun

STATUS

approved

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Last modified October 1 14:30 EDT 2014. Contains 247511 sequences.