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A142150
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The nonnegative integers (A001477) interleaved with zeros (A000004).
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9
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0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 0, 13, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 0, 19, 0, 20, 0, 21, 0, 22, 0, 23, 0, 24, 0, 25, 0, 26, 0, 27, 0, 28, 0, 29, 0, 30, 0, 31, 0, 32, 0, 33, 0, 34, 0, 35, 0, 36, 0, 37, 0, 38, 0, 39, 0, 40, 0, 41, 0, 42, 0, 43, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n) = XOR{k AND (n-k): 0<=k<=n}.
Contribution from Edgar Almeida Ribeiro (edgar.a.ribeiro(AT)gmail.com), May 19 2010: (Start)
a(n+1) = A000217(n) mod A000027(n+1).
a(n+1) = A000217(n) mod A001477(n+1). (End)
Number of vertical pairs in a wheel with n equal sections. - Wesley Ivan Hurt, Jan 22 2012
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LINKS
| R. Zumkeller, Logical Convolutions
Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
| a(n) = A027656(n-2). - Reinhard Zumkeller, Nov 05 2009
a(n) = (n/2)*0^(n mod 2); a(2*n)=n and a(2*n+1)=0.
a(n) = Floor(n^2/2) mod n [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Jul 29 2009]
a(n) = SUM((k mod 2)*((n-k) mod 2): 0<=k<=n). - Reinhard Zumkeller, Nov 05 2009
Contribution from Bruno Berselli, Oct 19 2010: (Start)
a(n) = n*(1+(-1)^n)/4.
G.f.: x^2/(1-x^2)^2.
a(n) = 2*a(n-2)-a(n-4).
Sum(a(i), i=0..n) = (2*n*(n+1)+(2*n+1)*(-1)^n-1)/16 (see A008805). (End)
a(n) = -a(-n) = A195034(n-1)-A195034(-n-1). - Bruno Berselli, Oct 12 2011
Contribution from Wesley Ivan Hurt, Jan 22 2012: (Start)
a(n) = (n/2)cos(Pi*n/2)^2.
a(n) = (n/2)ceil((-1/2)^n).
a(n) = (n/2)((n+1) mod 2).
a(n) = (n/2)abs(1+sum((-1)^ceil(i/2), i=1..n)).
a(n) = (n/2)+(n/2)floor(n/2)-(n/2)*ceil(n/2).
a(n) = (n/2)(1+sum((-1)^i, i=1..n)).
a(n) = (n/2)(1+sum(cos(Pi(i mod 2)), i=1..n)).
a(n) = (n/2)(n+1)-nfloor((n+1)/2).
a(n) = (n/2)ceil((n+1)/2)-(n/2)floor((n+1)/2).
a(n) = (n/2)ceil(frac((n+1)/2)).
a(n) = (n/2)abs(sin((Pi(n+1)/2)).
a(n) = (n/2)(1-sgn(floor(n/2)-ceil(n/2))^2).
a(n) = (n/2)sin(Pi*(n+1)/2)^2.
a(n) = (n/2)(1-ceil(frac(n/2))).
a(n) = (n/2)krondelta_{floor(n/2),ceil(n/2)}.
a(n) = (n/2)+(n/2)floor(n/2)+(n/2)floor(-n/2).
a(n) = (n/2)(1-ceil((n/2)-floor(n/2))).
a(n) = (n/2)-(n/2)ceil(n/2)-(n/2)ceil(-n/2).
a(n) = (n/2)-(n/2)frac(n/2)+(n/2)frac(-n/2).
(End)
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MAPLE
| Contribution from Wesley Ivan Hurt, Jan 22 2012: (Start)
a:=n->(n/2)*cos(Pi*n/2)^2;
a:=n->(n/2)*ceil((-1/2)^n);
a:=n->(n/2)*((n+1)mod 2);
a:=n->(n/2)*abs(1+sum((-1)^ceil(i/2), i=1..n));
a:=n->(n/2)+(n/2)*floor(n/2)-(n/2)*ceil(n/2);
a:=n->(n/2)*(1+sum((-1)^i, i=1..n));
a:=n->(n/2)*(1+sum(cos(Pi*(i mod 2)), i=1..n));
a:=n->(n/2)*(n+1)-n*floor((n+1)/2);
a:=n->(n/2)*ceil((n+1)/2)-(n/2)*floor((n+1)/2);
a:=n->(n/2)*ceil(frac((n+1)/2));
a:=n->(n/2)*abs(sin(Pi*(n+1)/2));
a:=n->(n/2)*(1-signum(floor(n/2)-ceil(n/2))^2);
a:=n->(n/2)*sin(Pi*(n+1)/2)^2;
a:=n->(n/2)*(1-ceil(frac(n/2)));
a:=n->(n/2)*piecewise(floor(n/2)=ceil(n/2), 1, 0);
a:=n->(n/2)+(n/2)*floor(n/2)+(n/2)*floor(-n/2);
a:=n->(n/2)*(1-ceil((n/2)-floor(n/2)));
a:=n->(n/2)-(n/2)*ceil(n/2)-(n/2)*ceil(-n/2);
a:=n->(n/2)-(n/2)*frac(n/2)+(n/2)*frac(-n/2);
(End)
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MATHEMATICA
| Table[Mod[Floor[n^2/2], n], {n, 1, 200}] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Jul 29 2009]
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CROSSREFS
| Cf. A003817, A000004, A142149, A086099, A142151, A001477.
Sequence in context: A108760 A137304 A027656 * A171181 A034948 A135472
Adjacent sequences: A142147 A142148 A142149 * A142151 A142152 A142153
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 15 2008
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