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A059841
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Repeat (1,0): a(n) = 1-n mod 2.
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78
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1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Period 2: repeat [1,0] (with offset 0).
When viewed as an array the row sum values are 1 1 1 2 3 3 3 4 5 5 5 6 ... A004525
This is the r=0 member of the r-family of sequences S_r(n) defined in A092184 where more information can be found.
Successive binomial transforms of this sequence : A011782, A007051, A007582, A081186, A081187, A081188, A081189, A081190, A060531, A081192
Characteristic function of even numbers: a(A005843(n))=1, a(A005408(n))=0. [From Reinhard Zumkeller, Sep 29 2008]
Hosoya index of the n-empty graph - Eric Weisstein, Jul 11 2011
This sequence is the Euler transformation of A185012. - Jason Kimberley, Oct 14 2011
The sequence 1, 0, 1, 0,... with offset 1 is also the parity of the natural numbers A000027. - Omar E, Pol, Jan 17 2012
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REFERENCES
| Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
| Eric Weisstein's World of Mathematics, Hosoya Index
Index to sequences with linear recurrences with constant coefficients, signature (0,1).
Index entries for characteristic functions
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FORMULA
| A059841(n)=1-A000035(n). - M. F. Hasler, Jan 13 2012
G.f.: 1/(1-x^2). E.g.f.: cosh(x). a(n)=(n+1)mod 2. a(n)=1/2 + (-1)^n/2. - Paul Barry, Mar 11 2003
Additive with a(p^e) = 1 if p = 2, 0 otherwise.
a(n) = (sin((n+1)*Pi/2))^2 = (cos(n*Pi/2))^2 with n>=0 - Paolo P. Lava, Nov 17 2006
a(n) = sum(k=0..n, (-1)^k*A038137(n,k) ) - Philippe DELEHAM, Nov 30 2006
a(n) = sum(k=1..n, (-1)^(n-k) ) for n > 0. - William A. Tedeschi, Aug 05 2011
E.g.f.: cosh(x) =1+x^2/(Q(0)-x^2); Q(k)=8k+2+x^2/(1+(2k+1)*(2k+2)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011
E.g.f.: cosh(x) =1/2*Q(0); Q(k)=1+1/(1-x^2/(x^2+(2k+1)*(2k+2)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011
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EXAMPLE
| Triangle begins :
1
0, 1
0, 1, 0
1, 0, 1, 0
1, 0, 1, 0, 1
0, 1, 0, 1, 0, 1
0, 1, 0, 1, 0, 1, 0
1, 0, 1, 0, 1, 0, 1, 0
1, 0, 1, 0, 1, 0, 1, 0, 1
0, 1, 0, 1, 0, 1, 0, 1, 0, 1
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
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MATHEMATICA
| CellularAutomaton[50, {{1}, 0}, 104, {All, {0}}] // Flatten [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
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PROG
| (PARI) a(n)=(n+1)%2;
(PARI) A059841(n)=!bittest(n, 0) \\ - M. F. Hasler, Jan 13 2012
(Haskell)
a059841 n = a059841_list !! n
a059841_list = cycle [1, 0] -- Reinhard Zumkeller, Dec 30 2011
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CROSSREFS
| Ones complement of A000035. Cf. A004525, A011782.
Characteristic function of multiples of g: A000007 (g=0), A000012 (g=1), this sequence (g=2), A079978 (g=3), A121262 (g=4), A079998 (g=5), A079979 (g=6), A082784 (g=7). - Jason Kimberley, Oct 14 2011
Sequence in context: A016213 A015757 A166698 * A056594 A101455 A091337
Adjacent sequences: A059838 A059839 A059840 * A059842 A059843 A059844
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Feb 25 2001
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EXTENSIONS
| Better definition from M. F. Hasler, Jan 13 2012.
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