A230419 Square array A(n,k) = difference of digit sums in factorial base representations (A007623) of n and k, n>=0, k>=0, read by antidiagonals; A(n,k) = A034968(n)-A034968(k).

0, 1, -1, 1, 0, -1, 2, 0, 0, -2, 2, 1, 0, -1, -2, 3, 1, 1, -1, -1, -3, 1, 2, 1, 0, -1, -2, -1, 2, 0, 2, 0, 0, -2, 0, -2, 2, 1, 0, 1, 0, -1, 0, -1, -2, 3, 1, 1, -1, 1, -1, 1, -1, -1, -3, 3, 2, 1, 0, -1, 0, 1, 0, -1, -2, -3, 4, 2, 2, 0, 0, -2, 2, 0, 0, -2, -2, -4

Offset: 0

Author

Antti Karttunen, Nov 10 2013

Keywords

• sign
• base
• tabl

Comments

Equivalently, A(n,k) = the sum of differences of digits in matching positions of the factorial base representations (A007623) of n and k.

Examples

			The top left corner array is:
   0,  1,  1,  2,  2,  3,  1,  2,  2,  3,  3, ...
  -1,  0,  0,  1,  1,  2,  0,  1,  1,  2,  2, ...
  -1,  0,  0,  1,  1,  2,  0,  1,  1,  2,  2, ...
  -2, -1, -1,  0,  0,  1, -1,  0,  0,  1,  1, ...
  -2, -1, -1,  0,  0,  1, -1,  0,  0,  1,  1, ...
  -3, -2, -2, -1, -1,  0, -2, -1, -1,  0,  0, ...
  -1,  0,  0,  1,  1,  2,  0,  1,  1,  2,  2, ...
  -2, -1, -1,  0,  0,  1, -1,  0,  0,  1,  1, ...
  -2, -1, -1,  0,  0,  1, -1,  0,  0,  1,  1, ...
  -3, -2, -2, -1, -1,  0, -2, -1, -1,  0,  0, ...
  -3, -2, -2, -1, -1,  0, -2, -1, -1,  0,  0, ...
  ...
		

Links

• Antti Karttunen, The first 121 antidiagonals of the table, flattened

Crossrefs

The topmost row: A034968 (and also the leftmost column negated).

Cf. A230415 (similar array which gives the number of differing digits).

Cf. A231713 (similar array which gives the sum of absolute differences).

Formula

A(col,row) = A034968(col)-A034968(row). [Where col is the column and row the row index of entry A(col,row)]

Equally, as a sequence, a(n) = A034968(A025581(n)) - A034968(A002262(n)).

For each entry, A(j,i) = -A(i,j), or as a sequence, a(A061579(n)) = -a(n). [The array is symmetric up to the sign of entries]

Also, for each entry A(i,j), abs(A(i,j)) <= A231713(i,j).