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A319047 Square array A(n,k) where column k is balanced (2k+1)-ary enumeration of integers; n>=0, k>=1, read by antidiagonals. 5
0, 0, 1, 0, 1, -1, 0, 1, 2, 3, 0, 1, 2, -2, 4, 0, 1, 2, 3, -1, 2, 0, 1, 2, 3, -3, 5, -3, 0, 1, 2, 3, 4, -2, 6, -2, 0, 1, 2, 3, 4, -4, -1, 7, -4, 0, 1, 2, 3, 4, 5, -3, 7, 3, 9, 0, 1, 2, 3, 4, 5, -5, -2, 8, 4, 10, 0, 1, 2, 3, 4, 5, 6, -4, -1, 9, 10, 8, 0, 1, 2, 3, 4, 5, 6, -6, -3, 9, 10, 11, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Alois P. Heinz, Antidiagonals n = 0..200, flattened

Wikipedia, Balanced ternary

EXAMPLE

Square array A(n,k) begins:

   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ...

   1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...

  -1,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2, ...

   3, -2,  3,  3,  3,  3,  3,  3,  3,  3,  3, ...

   4, -1, -3,  4,  4,  4,  4,  4,  4,  4,  4, ...

   2,  5, -2, -4,  5,  5,  5,  5,  5,  5,  5, ...

  -3,  6, -1, -3, -5,  6,  6,  6,  6,  6,  6, ...

  -2,  7,  7, -2, -4, -6,  7,  7,  7,  7,  7, ...

  -4,  3,  8, -1, -3, -5, -7,  8,  8,  8,  8, ...

   9,  4,  9,  9, -2, -4, -6, -8,  9,  9,  9, ...

  10, 10, 10, 10, -1, -3, -5, -7, -9, 10, 10, ...

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 0,

      (b-> b*A(iquo(n, b), k)+mods(n, b))(2*k+1))

    end:

seq(seq(A(n, 1+d-n), n=0..d), d=0..14);

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 0, With[{b = 2k+1},

     b*A[Quotient[n, b], k] + Mod[n, b, -Quotient[b-1, 2]]]];

Table[Table[A[n, 1+d-n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-Fran├žois Alcover, Feb 09 2021, after Alois P. Heinz *)

CROSSREFS

Columns k=1-4 give: A117966, A309991, A309995, A316823.

A(n,n+1) gives A001477.

A(n+1,n) gives A001478 (for n>0).

Sequence in context: A106728 A292603 A308880 * A276335 A189480 A010873

Adjacent sequences:  A319044 A319045 A319046 * A319048 A319049 A319050

KEYWORD

sign,look,hear,tabl

AUTHOR

Alois P. Heinz, Aug 26 2019

STATUS

approved

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Last modified May 12 23:09 EDT 2021. Contains 343829 sequences. (Running on oeis4.)