A372345 - OEIS

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.

%I #10 Apr 30 2024 14:48:42

%S 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,

%T 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,

%U 1,0,3,4,4,3,0,1,1,0,0,1,0,1,9,4,6,4,9,1,0,1,0

%N 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.

%C 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.

%H Rémy Sigrist, <a href="/A372345/b372345.txt">Table of n, a(n) for n = 0..10010</a>

%H Rémy Sigrist, <a href="/A372345/a372345.png">Scatterplot of (n, k) such that A(n, k) = 0 and n, k <= 2^10</a>

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

%e Array A(n, k) begins:

%e n\k | 0 1 2 3 4 5 6 7 8 9 10

%e ----+--------------------------------------

%e 0 | 0 0 0 0 0 0 0 0 0 0 0

%e 1 | 0 0 1 1 0 0 1 1 0 0 1

%e 2 | 0 1 0 1 3 4 3 4 0 1 0

%e 3 | 0 1 1 2 3 4 4 5 0 1 1

%e 4 | 0 0 3 3 0 0 3 3 9 9 12

%e 5 | 0 0 4 4 0 0 4 4 9 9 13

%e 6 | 0 1 3 4 3 4 6 7 9 10 12

%e 7 | 0 1 4 5 3 4 7 8 9 10 13

%e 8 | 0 0 0 0 9 9 9 9 0 0 0

%e 9 | 0 0 1 1 9 9 10 10 0 0 1

%e 10 | 0 1 0 1 12 13 12 13 0 1 0

%o (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); }

%Y See A372344 for a similar sequence.

%K nonn,base,tabl

%O 0,24

%A _Rémy Sigrist_, Apr 28 2024