

A237420


If n is odd, then a(n) = 0; otherwise, a(n) = n.


3



0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74
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OFFSET

0,3


COMMENTS

Normally the OEIS excludes sequences in which every other term is zero. But there are exceptions for especially important sequences like this one.  N. J. A. Sloane, Feb 27 2014
Essentially the factorial expansion of exp(1): exp(1) = sum(n>=1, a(n)/(n+1)! ). [Joerg Arndt, Mar 13 2014]
a(n) is the number of m < n for which a(m) has the same parity as n. For instance, a(4) = 4 because 4 has the same parity as a(0), a(1), a(2), and a(3).  Alec Jones, May 16 2016


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019)
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1).


FORMULA

O.g.f.: 2*x^2/(1x^2)^2.
E.g.f.: x*sinh(x).  Robert Israel, Aug 27 2015
a(n) = 2*a(n2)  a(n4) for n>4.
a(n) = 2*A142150(n) = (1+(1)^n)*n/2 = n*((n1) mod 2).
a(n) = floor(n^(1)^n) for n>1.  Ilya Gutkovskiy, Aug 27 2015
Sum_{i=1..n} a(i) = A110660(n).  Bruno Berselli, Feb 27 2014
a(n) = 1 + ceiling((n + 1)^(sin(Pi*n/2) + cos(Pi*n))).  Lechoslaw Ratajczak, Nov 06 2016


MAPLE

seq(op([0, 2*i]), i=1..30); # Robert Israel, Aug 27 2015


MATHEMATICA

Table[If[OddQ[n], 0, n], {n, 80}]
CoefficientList[Series[2 x /(1  x^2)^2, {x, 0, 80}], x]
LinearRecurrence[{0, 2, 0, 1}, {0, 0, 2, 0}, 75] (* Robert G. Wilson v, Nov 11 2016 *)


PROG

(MAGMA) [IsOdd(n) select 0 else n: n in [1..80]];
(MAGMA) [(1+(1)^n)*n/2: n in [1..80]];
(MAGMA) &cat [[n, 0]: n in [0..80 by 2]]; // Bruno Berselli, Nov 11 2016
(PARI) a(n)=if(n%2==0, n, 0) \\ Anders HellstrÃ¶m, Aug 27 2015


CROSSREFS

Cf. A005843, A110660, A142150, A193356.
Sequence in context: A319813 A071648 A001613 * A130891 A091371 A144775
Adjacent sequences: A237417 A237418 A237419 * A237421 A237422 A237423


KEYWORD

nonn,easy


AUTHOR

Vincenzo Librandi, Feb 24 2014


EXTENSIONS

Edited by Bruno Berselli, Feb 27 2014


STATUS

approved



