A372345 Square array A(n, k), n, k >= 0, read by upwards antidiagonals; for any n, k >= 0 with respective binary expansions Sum_{i >= 0} b_i * 2^i and Sum_{i >= 0} c_i * 2^i, A(n, k) = Sum_{i >= 0} (b_{i+1} * c_i + b_i * c_{i+1}) * 3^i.

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 3, 2, 3, 0, 0, 0, 1, 4, 3, 3, 4, 1, 0, 0, 1, 3, 4, 0, 4, 3, 1, 0, 0, 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 5, 3, 0, 3, 5, 0, 0, 0, 0, 1, 1, 0, 3, 4, 4, 3, 0, 1, 1, 0, 0, 1, 0, 1, 9, 4, 6, 4, 9, 1, 0, 1, 0

Offset

0,24

Comments

The digits in the ternary expansion of A(n, k) correspond to permanents of 2 X 2 matrices made up of binary digits of n and k.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Rémy Sigrist, Scatterplot of (n, k) such that A(n, k) = 0 and n, k <= 2^10

Formula

A(k, n) = A(n, k).

Example

Array A(n, k) begins:
  n\k | 0  1  2  3   4   5   6   7  8   9  10
  ----+--------------------------------------
    0 | 0  0  0  0   0   0   0   0  0   0   0
    1 | 0  0  1  1   0   0   1   1  0   0   1
    2 | 0  1  0  1   3   4   3   4  0   1   0
    3 | 0  1  1  2   3   4   4   5  0   1   1
    4 | 0  0  3  3   0   0   3   3  9   9  12
    5 | 0  0  4  4   0   0   4   4  9   9  13
    6 | 0  1  3  4   3   4   6   7  9  10  12
    7 | 0  1  4  5   3   4   7   8  9  10  13
    8 | 0  0  0  0   9   9   9   9  0   0   0
    9 | 0  0  1  1   9   9  10  10  0   0   1
   10 | 0  1  0  1  12  13  12  13  0   1   0

Prog

(PARI) A(n, k) = { my (v = 0, t = 1); while (n && k, v += (bittest(n, 1)*bittest(k, 0) + bittest(n, 0)*bittest(k, 1)) * t; n \= 2; k \= 2; t *= 3; ); return (v); }

Crossrefs

See A372344 for a similar sequence.

Sequence in context: A108032 A053370 A016458 * A058513 A319650 A285736

Adjacent sequences: A372342 A372343 A372344 * A372346 A372347 A372348

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Apr 28 2024

Status

approved