A303404 -id:A303404 - cp's OEIS frontend

A318190 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1) - 2a(n), a(2n+1) = 2n - a(2n).

0, 1, -1, 3, 5, -1, -7, 13, 3, 5, 7, 3, 17, -5, -31, 45, 39, -23, -33, 51, 37, -17, -23, 45, 11, 13, 23, 3, 65, -37, -127, 157, 79, -47, -1, 35, 101, -65, -167, 205, 131, -91, -57, 99, 145, -101, -191, 237, 215, -167, -193, 243, 197, -145, -151, 205, 75, -19, 55, 3, 257, -197, -511, 573, 415, -351, -257, 323, 325

Offset: 0

Altug Alkan, Aug 20 2018

Altug Alkan, Table of n, a(n) for n = 0..10000
Altug Alkan, A scatterplot of a(n) for n <= 10^5

Cf. A002487, A303404.

[0] cat [n eq 1 select 1 else n mod 2 eq 0 select Self(n-1)-2*Self(n div 2) else n-1 - Self(n-1): n in [1..70]]; // Vincenzo Librandi, Aug 28 2018

f:= proc(n) option remember;
  if n::even then procname(n-1) - 2*procname(n/2)
  else n-1-procname(n-1)
  fi
end proc:
f(0):= 0: f(1):= 1:
map(f, [$0..100]); # Robert Israel, Aug 28 2018

a[0]=0; a[1]=1; a[n_] := a[n] = If[EvenQ[n], a[n-1] - 2 a[n/2], n-1 - a[n - 1]]; Array[a, 70, 0] (* Giovanni Resta, Aug 27 2018 *)

a(n)=if(n<=1, n, if(n%2==0, a(n-1)-2*a(n/2), n-1-a(n-1)));

a = vector(99); print1 (0", "); for(n=1, #a, print1 (a[n]=if(n==1, 1, if(n%2, n-1-a[n-1], a[n-1]-2*a[n/2]))", "));

G.f. g(x) satisfies g(x) = (x+x^5)/(1-x^2)^2 - x*g(-x) - 2*g(x^2). - Robert Israel, Aug 28 2018

A318163 a(0) = a(3) = 0, a(1) = a(2) = 1; for n >= 2, a(2n) = -a(n-1) and a(2n+1) = -a(n-1)-a(n).

Original entry on oeis.org

0, 1, 1, 0, -1, -2, -1, -1, 0, 1, 1, 3, 2, 3, 1, 2, 1, 1, 0, -1, -1, -2, -1, -4, -3, -5, -2, -5, -3, -4, -1, -3, -2, -3, -1, -2, -1, -1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, -1, -1, -2, -1, -3, -2, -3, -1, -4, -3, -5, -2, -5, -3, -4, -1, -6, -5, -9, -4, -11, -7

Offset: 0

Altug Alkan, Aug 19 2018

Inspired by A002487.
Alternatively, a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1) - a(2*n-2), a(2*n+1) = a(2*n) - a(n). Note that if b(0) = 0, b(1) = 1; for n >= 1, b(2*n) = b(2*n-1) - b(n), b(2*n+1) = b(2*n) - b(2*n-1), then b(n) + A213369(n+1) = 0 for all n >= 1.
The main block structure of this sequence is described by A020714.

Altug Alkan, Table of n, a(n) for n = 0..20480
Altug Alkan, A scatterplot of a(n) for n <= 5*2^12
Altug Alkan, A scatterplot of first differences of a(n) for n <= 5*2^13

Cf. A002487, A020944, A213369, A303404.

a[0]=a[3]=0; a[1]=a[2]=1; a[n_] := a[n] = If[EvenQ[n], -a[n/2-1], -a[(n-1)/2 - 1] - a[(n-1)/2]]; Array[a, 101, 0] (* Giovanni Resta, Aug 27 2018 *)

a = vector(100); print1(0", "); for(k=1, #a, print1 (a[k]=if(k<=2,1, my (n=k\2); if (k%2==0, -a[n-1], a[2*n]-a[n]))", "));

a(5*2^k-2) = 0 for all k >= 0.

A319010 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1), a(2n+1) = 2(n - a(n)).

Original entry on oeis.org

0, 1, 1, 0, 0, 2, 2, 6, 6, 8, 8, 6, 6, 8, 8, 2, 2, 4, 4, 2, 2, 4, 4, 10, 10, 12, 12, 10, 10, 12, 12, 26, 26, 28, 28, 26, 26, 28, 28, 34, 34, 36, 36, 34, 34, 36, 36, 26, 26, 28, 28, 26, 26, 28, 28, 34, 34, 36, 36, 34, 34, 36, 36, 10, 10, 12, 12, 10, 10, 12, 12, 18, 18, 20, 20, 18, 18, 20, 20

Offset: 0

Altug Alkan, Sep 07 2018

Altug Alkan, Table of n, a(n) for n = 0..8190
Altug Alkan, An image from line plot of (a(n), A318190(n)) for n = 1..2^12-2

Cf. A002487, A303404, A318190.

a = vector(100); print1(0", "); for(k=1, #a, print1 (a[k]=if(k==1, 1, my (n=k\2); if (k%2==0, a[2*n-1], 2*(n-a[n])))", "));

a(n) = if(n<=1, n, if(n%2==0, a(n-1),2*((n-1)/2-a((n-1)/2))));

cp's OEIS Frontend

A318190 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1) - 2a(n), a(2n+1) = 2n - a(2n).

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A318163 a(0) = a(3) = 0, a(1) = a(2) = 1; for n >= 2, a(2n) = -a(n-1) and a(2n+1) = -a(n-1)-a(n).

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A319010 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1), a(2n+1) = 2(n - a(n)).

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PARI

cp's OEIS Frontend

A318190 a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1) - 2*a(n), a(2*n+1) = 2*n - a(2*n).

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Programs

Magma

Maple

Mathematica

PARI

PARI

Formula

A318163 a(0) = a(3) = 0, a(1) = a(2) = 1; for n >= 2, a(2*n) = -a(n-1) and a(2*n+1) = -a(n-1)-a(n).

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Crossrefs

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Mathematica

PARI

Formula

A319010 a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1), a(2*n+1) = 2*(n - a(n)).

Views

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Programs

PARI

PARI

A318190 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1) - 2a(n), a(2n+1) = 2n - a(2n).

A318163 a(0) = a(3) = 0, a(1) = a(2) = 1; for n >= 2, a(2n) = -a(n-1) and a(2n+1) = -a(n-1)-a(n).

A319010 a(0) = 0, a(1) = 1; for n >= 1, a(2n) = a(2n-1), a(2n+1) = 2(n - a(n)).