A135689 -id:A135689 - cp's OEIS frontend

A135690 a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.

0, 1, -1, 2, -4, -2, -6, 0, -12, -8, -16, -4, -28, -20, -36, -12, -60, -44, -76, -28, -124, -92, -156, -60, -252, -188, -316, -124, -508, -380, -636, -252, -1020, -764, -1276, -508, -2044, -1532, -2556, -1020, -4092, -3068, -5116, -2044, -8188, -6140, -10236, -4092, -16380, -12284, -20476

Offset: 0

Roger L. Bagula, Feb 19 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2).

Cf. A135689, A135692.

a[0] = 0; a[1] = 1; a[2] = -1; a[3] = 2; a[n_]:= a[n]= If[Mod[n, 2]==0, a[n-2] - (a[n-1] -a[n-2]), a[n-1] -(a[n-3] -a[n-4])]; Table[a[n], {n, 0, 60}]

a(n) = 4 - [4,3,5,2][n%4+1] << (n>>2); \\ Kevin Ryde, Nov 26 2021

@CachedFunction
def A135690(n):
    if (n<2): return n
    elif (n<4): return (-1)^(n+1)*(n-1)
    elif (n%2==0): return A135690(n-2) - (A135690(n-1) - A135690(n-2))
    else: return A135690(n-1) - (A135690(n-3) - A135690(n-4))
[A135690(n) for n in (0..60)] # G. C. Greubel, Nov 24 2021

G.f.: x*(1-2*x)*(1+3*x^2)/((1-x)*(1-2*x^4)). - Colin Barker, Jan 26 2013

a(n) = 4 - C*2^floor(n/4), where C = 4,3,5,2 according as n mod 4 = 0,1,2,3 respectively. - Kevin Ryde, Nov 26 2021

Edited by G. C. Greubel and Kevin Ryde, Nov 24 2021

A135692 a(n) = a(n-2) - 2( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

Original entry on oeis.org

0, 1, -2, -4, 4, 6, 8, 6, -8, -2, -12, -8, -16, -32, -12, -16, 16, 12, 4, 8, 24, 52, 16, 4, 32, 52, 64, 56, 24, 40, 32, 64, -32, -72, -24, -16, -8, -72, -16, -8, -48, -32, -104, -112, -32, -64, -8, -64, -64, 8, -104, -80, -128, -184, -112, -152, -48, -72, -80, -64, -64, 0, -128, -160, 64, 80, 144, 80, 48, 240, 32, 112, 16, -80

Offset: 0

Roger L. Bagula, Feb 21 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Kevin Ryde, PARI/GP Code and Notes

Cf. A135689, A135690.

a[n_]:= a[n]= If[n<2, n, If[n<4, -2^(n-1), If[Mod[n, 2]==0, a[n-2] - 2*( a[Floor[n/2]] - a[Abs[Floor[n/2] -1]]), a[n-1] - 2*(a[Abs[Floor[n/2] -2]] - a[Abs[Floor[n/2] -3]]) ]]];
Table[a[n], {n, 0, 80}]

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@CachedFunction
def A135692(n):
    if (n<2): return n
    elif (n<4): return -2^(n-1)
    elif (n%2==0): return A135692(n-2) - 2*(A135692(n//2) - A135692(abs(n//2 -1)))
    else: return A135692(n-1) - 2*(A135692(abs(n//2 -2)) - A135692(abs(n//2 -3)))
[A135692(n) for n in (0..80)] # G. C. Greubel, Nov 24 2021

a(n) = a(n-2) - 2*( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2*( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

Edited by G. C. Greubel, Nov 24 2021

A135564 a(n) defined by a(2n) = a(2n-2) - (a(n) - 2a(n-1) + a(n-2)) for n > 2, a(2n+1) = a(2n) - (a(n-2) - 2a(n-3) + a(n-4)), for n > 3, with a(0)=0, a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=-3, a(6)=4, a(7)=2.

Original entry on oeis.org

0, 1, 3, -1, -2, -3, 4, 2, 1, 0, 1, 7, -7, -10, 2, 2, 1, -7, 1, 10, -1, -2, -6, -6, 14, 12, 3, -2, -12, 8, 0, -11, 1, -14, 8, 20, -8, -7, -9, -2, 11, -5, 1, 0, 4, 24, 0, -10, -20, -17, 2, -2, 9, -11, 5, 27, 10, 17, -20, -24, 8, 13, 11, -19, -12, 16, 15, 18, -22, -45, -12, 15, 28, -9, -1, 9, 2, 42, -7, -36, -13, -10, 16, 7, -6, -12, 1, 30, -4

Offset: 0

Roger L. Bagula, Feb 23 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A122581, A135689, A135690, A135692.

a[0]:=0; a[1]:=1; a[2]:=3; a[3]:=-1; a[4]:=-2; a[5]:=-3; a[6]:=4; a[7]:=2;
a[n_]:= a[n]= If[Mod[n, 2]==0, a[n-2] -a[n/2] +2*a[n/2 -1] -a[n/2 -2], a[n-1] -a[(n-1)/2 -2] +2*a[(n-1)/2 -3] -a[(n-1)/2 -4]];
Table[a[n], {n, 0, 100}]

@CachedFunction
def a(n): # A135564
    if (n<8): return [0, 1, 3, -1, -2, -3, 4, 2][n]
    elif ((n%2)==0): return a(n-2) - a(n/2) + 2*a(n/2 - 1) - a(n/2 -2)
    else: return a(n-1) - a((n-1)/2 - 2) + 2*a((n-1)/2 - 3) - a((n-1)/2 -4)
[a(n) for n in (0..100)] # G. C. Greubel, Nov 26 2021

a(n) = a(n-2) - (a(floor(n/2)) - 2*a(abs(floor(n/2) -1)) + a(abs(floor(n/2) -2)) ) if (n mod 2) = 0, otherwise a(n-1) - (a(abs(floor(n/2) - 2)) - 2*a(abs(floor(n/2) - 3)) + a(abs(floor(n/2) - 4)).
a(2*n) = a(2*n-2) - (a(n) - 2*a(n-1) + a(n-2)), for n > 2.
a(2*n+1) = a(2*n) - (a(n-2) - 2*a(n-3) + a(n-4)), for n > 3.

Edited by G. C. Greubel, Nov 28 2021

cp's OEIS Frontend

A135690 a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.

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A135692 a(n) = a(n-2) - 2( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

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A135564 a(n) defined by a(2n) = a(2n-2) - (a(n) - 2a(n-1) + a(n-2)) for n > 2, a(2n+1) = a(2n) - (a(n-2) - 2a(n-3) + a(n-4)), for n > 3, with a(0)=0, a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=-3, a(6)=4, a(7)=2.

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cp's OEIS Frontend

A135690 a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

Extensions

A135692 a(n) = a(n-2) - 2*( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2*( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

Extensions

A135564 a(n) defined by a(2*n) = a(2*n-2) - (a(n) - 2*a(n-1) + a(n-2)) for n > 2, a(2*n+1) = a(2*n) - (a(n-2) - 2*a(n-3) + a(n-4)), for n > 3, with a(0)=0, a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=-3, a(6)=4, a(7)=2.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Sage

Formula

Extensions

A135692 a(n) = a(n-2) - 2( a(floor(n/2)) - a(abs(floor(n/2) - 1)) ) if (n mod 2) = 0, otherwise a(n-1) - 2( a(abs(floor(n/2) - 2)) - a(abs(floor(n/2) - 3)) ), with a(0) = 0, a(1) = 1, a(2) = -2, a(3) = -4.

A135564 a(n) defined by a(2n) = a(2n-2) - (a(n) - 2a(n-1) + a(n-2)) for n > 2, a(2n+1) = a(2n) - (a(n-2) - 2a(n-3) + a(n-4)), for n > 3, with a(0)=0, a(1)=1, a(2)=3, a(3)=-1, a(4)=-2, a(5)=-3, a(6)=4, a(7)=2.