A372359 Array read by upward antidiagonals: A(n, k) = A372358(A372282(n, k)), n,k >= 1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 24, 4, 0, 0, 0, 256, 32, 6, 0, 0, 0, 0, 6144, 16, 0, 0, 0, 0, 0, 16777216, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 1408, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6144, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16777216, 0, 88, 12

Offset: 1

Author

Antti Karttunen, May 01 2024

Keywords

• nonn
• tabl

Comments

Zeros occur in the same locations as where they occur in A372353 and where 1's occur in array A372287.

Examples

			Array begins:
n\k| 1  2  3    4     5   6  7     8  9    10 11  12         13             14
---+----------------------------------------------------------------------------
1  | 0, 0, 0,   2,    4,  6, 0,    2, 4,    6, 0,  2,        12,            14,
2  | 0, 0, 0,  24,   32, 16, 0,    8, 0,   32, 0, 88,        96,           112,
3  | 0, 0, 0, 256, 6144,  0, 0, 1408, 0, 6144, 0,  0,      8192,          2560,
4  | 0, 0, 0,   0, 2^24,  0, 0,    0, 0, 2^24, 0,  0, 402653184,       6815744,
5  | 0, 0, 0,   0,    0,  0, 0,    0, 0,    0, 0,  0,      2^56, 4947802324992,
6  | 0, 0, 0,   0,    0,  0, 0,    0, 0,    0, 0,  0,         0,     31 * 2^79,
where 2^56 = 72057594037927936 and 31 * 2^79 = 18738350204026752207945728.
		

Crossrefs

Cf. A003987, A086893, A371094, A372282, A372287, A372354, A372358, A372360 (binary weights).

Cf. also A372353.

Programs

PARI

up_to = 91;
A000523(n) = logint(n,2);
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
A372358(n) = bitxor(A086893(1+A000523(n)),n);
A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
A372359sq(n,k) = A372358(A372282sq(n,k));
A372359list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A372359sq((a-(col-1)),col))); (v); };
v372359 = A372359list(up_to);
A372359(n) = v372359[n];

Formula

A(n, k) = A372282(n,k) XOR A086893(1+A372354(n, k)), where XOR is bitwise-xor, A003987.