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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
Reinhard Zumkeller, Logical Convolutions
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
Sequence in context: A234585 A257770 A027656 * A276457 A171181 A364788
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.)