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A142150
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The nonnegative integers interleaved with zeros.
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42
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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
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OFFSET
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0,5
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COMMENTS
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Number of vertical pairs in a wheel with n equal sections. - Wesley Ivan Hurt, Jan 22 2012
Number of even terms of n-th row in the triangles A162610 and A209297. - Reinhard Zumkeller, Jan 19 2013
Also the result of writing n-1 in base 2 and multiplying the last digit with the number with its last digit removed. See A115273 and A257844-A257850 for generalization to other bases. - M. F. Hasler, May 10 2015
Also follows the rule: a(n+1) is the number of terms that are identical with a(n) for a(0..n-1). - Marc Morgenegg, Jul 08 2019
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
R. Zumkeller, Logical Convolutions
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
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a(n) = XOR{k AND (n-k): 0<=k<=n}.
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. [Enrique Pérez Herrero, Jul 29 2009]
a(n) = A027656(n-2). - Reinhard Zumkeller, Nov 05 2009
a(n) = sum(k=0..n, (k mod 2)*((n-k) mod 2)). - Reinhard Zumkeller, Nov 05 2009
a(n+1) = A000217(n) mod A000027(n+1) = A000217(n) mod A001477(n+1). [Edgar Almeida Ribeiro (edgar.a.ribeiro(AT)gmail.com), May 19 2010]
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
a(n) = A000326(n) - A191967(n). - Reinhard Zumkeller, Jul 07 2012
a(n) = n*(n+1)/2 mod n, for n>=1. - Paolo P. Lava, Jan 07 2013
a(n) = sum_{i=1..n} floor((2i-n)/2). - Wesley Ivan Hurt, Aug 21 2014
a(n-1) = floor(n/2)*(n mod 2), where (n mod 2) is the parity of n, or remainder of division by 2. - M. F. Hasler, May 10 2015
a(n) = A158416(n) - 1. - Filip Zaludek, Oct 30 2016
E.g.f.: x*sinh(x)/2. - Ilya Gutkovskiy, Oct 30 2016
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MAPLE
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A142150:=n->n*(1+(-1)^n)/4: seq(A142150(n), n=0..100); # Wesley Ivan Hurt, Aug 21 2014
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MATHEMATICA
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Table[Mod[Floor[n^2/2], n], {n, 200}] (* Enrique Pérez Herrero, Jul 29 2009 *)
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PROG
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(Haskell)
a142150 = uncurry (*) . (`divMod` 2) . (+ 1)
a142150_list = scanl (+) 0 a001057_list
-- Reinhard Zumkeller, Apr 02 2012
(MAGMA) [n*(1+(-1)^n)/4 : n in [0..100]]; // Wesley Ivan Hurt, Aug 21 2014
(PARI) a(n)=!bittest(n, 0)*n>>1 \\ M. F. Hasler, May 10 2015
(MAGMA) &cat[[n, 0]: n in [0..50]]; // Vincenzo Librandi, Oct 31 2016
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CROSSREFS
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Cf. A000004, A000027, A000217, A000326, A001057, A001477, A003817, A008805, A027656, A086099, A142149, A142151, A162610, A191967, A195034, A209297.
Sequence in context: A234585 A257770 A027656 * A276457 A171181 A309261
Adjacent sequences: A142147 A142148 A142149 * A142151 A142152 A142153
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KEYWORD
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nonn,easy
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AUTHOR
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Reinhard Zumkeller, Jul 15 2008
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STATUS
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approved
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