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A142150 The nonnegative integers interleaved with zeros. 41
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

LINKS

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).

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(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

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 *)

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

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 A034948

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 February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)