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 A142150 The nonnegative integers interleaved with 0's. 47
 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; text; internal format)
 OFFSET 0,5 COMMENTS 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Reinhard Zumkeller, Logical Convolutions Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA 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_{i=0..n} a(i) = (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) = Sum_{i=1..n} floor((2*i-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 MAPLE A142150:=n->n*(1+(-1)^n)/4: seq(A142150(n), n=0..100); # Wesley Ivan Hurt, Aug 21 2014 MATHEMATICA Table[Mod[Floor[n^2/2], n], {n, 200}] (* Enrique Pérez Herrero, Jul 29 2009 *) Riffle[Range[0, 50], 0] (* Paolo Xausa, Feb 08 2024 *) PROG (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 (Python) def A142150(n): return (n+1>>1)*(n&1^1) # Chai Wah Wu, Jan 19 2023 CROSSREFS 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 A364788 Adjacent sequences: A142147 A142148 A142149 * A142151 A142152 A142153 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, Jul 15 2008 STATUS approved

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Last modified April 16 23:37 EDT 2024. Contains 371756 sequences. (Running on oeis4.)