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A194880 The numerators of the inverse Akiyama-Tanigawa algorithm from A001045(n). 3
0, -1, -1, -4, -5, -2, -7, -8, -3, -10, -11, -4, -13, -14, -5, -16, -17, -6, -19, -20, -7, -22, -23, -8, -25, -26, -9, -28, -29, -10, -31, -32, -11, -34, -35, -12, -37, -38, -13, -40, -41, -14, -43, -44, -15, -46, -47, -16, -49, -50, -17, -52, -53, -18, -55, -56, -19, -58, -59, -20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

0,  -1, -1, -4/3, -5/3, -2, -7/3, -8/3, -3, -10/3, -11/3, -4, -13/4, -14/3, -5,    = a(n)/b(n),

1,    0,  1,  4/3,  5/3,  2,  7/3,  8/3,  3,

1,   -2, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,

3,   -2,  1,  4/3,  5/3,  2,  7/3,  8/3,  3,

5,   -6, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,

11, -10,  1,  4/3,  5/3,  2,  7/3,  8/3,  3,

21, -22, -1, -4/3, -5/3, -2, -7/3, -8/3, -3,

Vertical: A001045(n), -A078008(n), (-1)^(n+1)*A000012(n), (-1)^(n+1)*A010709(n)/A010701(n), (-1)^(n+1)*A010716(n+1)/A010701(n), A007395(n), .. .

a(n)=0, 1 before (-A145064(n+1)=-A051176(n+3).

b(n)=1, 1 before A169609(n). b(n)=1, 1, 1 before A144437(n+1).

a(n+5)-a(n+2)=b(n+5)  (=-1,-3,-3,=-A169609(n)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

D. Merlini, R. Sprugnoli, M. C. Verri, The Akiyama-Tanigawa Transformation, Integers, 5 (1) (2005) #A05.

FORMULA

a(3*n)=-3*n-1 except a(0)=0; a(3*n+1=-3*n-2 except a(1)=-1; a(3*n+2)=-n-1.

MATHEMATICA

a[0]=0; a[1]=-1; a[n_] := (-n-1)/Max[1, 2*Mod[n, 3]-1]; Table[a[n], {n, 0, 59}] (* Jean-Fran├žois Alcover, Sep 18 2012 *)

CROSSREFS

Sequence in context: A090201 A130144 A118472 * A111624 A019815 A281143

Adjacent sequences:  A194877 A194878 A194879 * A194881 A194882 A194883

KEYWORD

sign,tabl,frac

AUTHOR

Paul Curtz, Sep 07 2011

STATUS

approved

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Last modified February 16 21:26 EST 2020. Contains 331975 sequences. (Running on oeis4.)