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 A218856 Real part of the arithmetic derivative for the triangle of Gaussian integers z = r + i*I. 4
 0, 0, 0, 0, 0, 2, 1, 2, 0, -2, -1, -2, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 8, 3, 6, 3, 8, 2, 0, -2, -8, -3, -6, -3, -8, -2, 0, 2, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, -3, -1, -1, -1, -1, -3, 0, 0, 0, 0, 8, 4, 8, 4, 8, 4, 6, 3, 2, -1, -2, -3, -8, -4, -8, -4, -8, -4, -6, -3, -2, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS For n > 0, the 4*n terms in row n are computed starting at (n,0) and proceeding counterclockwise (n-1,1), (n-2,2), ..., (0,n), (-1,n-1), (-2,n-2), ..., (-n,0), (-n+1,-1), (-n+2,-2), ..., (0,-n), (1,-n+1), (2,-n+2), ..., (n-1,-1). See the two-dimensional plot to see both the real and the imaginary parts. The imaginary part is in A218857. Consult A099379 for the arithmetic derivative of Gaussian integers. LINKS T. D. Noe, Rows n = 0..50 of triangle, flattened T. D. Noe, 2-d plots of the derivative for n = 3..25 EXAMPLE Triangle: 0, 0, 0, 0, 0, 2, 1, 2, 0, -2, -1, -2, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 8, 3, 6, 3, 8, 2, 0, -2, -8, -3, -6, -3, -8, -2, 0, 2, 3, 1, 1, 1, 1, 3, 0, 0, 0, 0, -3, -1, -1, -1, -1, -3, 0, 0, 0, 0, 8, 4, 8, 4, 8, 4, 6, 3, 2, -1, -2, -3, -8, -4, -8, -4, -8, -4, -6, -3, -2, 1, 2, 3 MATHEMATICA di[0]=0; di[1]=0; di[ -1]=0; di[I]=0; di[ -I]=0; di[n_] := Module[{f, unt}, f=FactorInteger[n, GaussianIntegers->True]; unt=(Abs[f[[1, 1]]]==1); If[unt, f=Delete[f, 1]]; f=Transpose[f]; Plus@@(n*f[[2]]/f[[1]])]; Table[t = Join[Table[di[n - i + I*i], {i, 0, n}], Table[di[i - n + I*i], {i, n - 1, 0, -1}], Table[di[i - n - I*i], {i, 1, n}], Table[di[n - i - I*i], {i, n - 1, 1, -1}]]; Re[t], {n, 0, 6}] CROSSREFS Cf. A099379, A099380. Sequence in context: A295664 A250213 A033794 * A101665 A229951 A165034 Adjacent sequences:  A218853 A218854 A218855 * A218857 A218858 A218859 KEYWORD sign,tabf AUTHOR T. D. Noe, Nov 12 2012 STATUS approved

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Last modified October 14 11:58 EDT 2019. Contains 328000 sequences. (Running on oeis4.)