A372361 Array read by upward antidiagonals: A(n, k) = A372358(A372283(n, k)), n,k >= 1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 4, 2, 6, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 22, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 22, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 14

Offset: 1

Author

Antti Karttunen, May 01 2024

Keywords

• nonn
• tabl

Examples

			Array begins:
n\k| 1  2  3  4  5  6  7   8  9 10 11  12  13   14 15   16  17  18  19  20
---+------------------------------------------------------------------------
1  | 0, 0, 0, 2, 4, 6, 0,  2, 4, 6, 0,  2, 12,  14, 8,  10, 20, 22, 16, 18,
2  | 0, 0, 0, 6, 2, 4, 0,  2, 0, 8, 0, 22,  6,  28, 6,  26, 12,  0,  2, 14,
3  | 0, 0, 0, 4, 6, 0, 0, 22, 0, 6, 0,  0,  8,  10, 4,  18,  6,  0,  6, 12,
4  | 0, 0, 0, 0, 4, 0, 0,  0, 0, 4, 0,  0,  6,  26, 0,  62,  8,  0,  4, 22,
5  | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  4,  18, 0, 116,  6,  0,  0, 48,
6  | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  62, 0,  44,  4,  0,  0,  6,
7  | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 116, 0,  14,  0,  0,  0,  8,
8  | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  44, 0,  92,  0,  0,  0,  6,
9  | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  14, 0,  50,  0,  0,  0,  4,
10 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  92, 0,  78,  0,  0,  0,  0,
11 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  50, 0,  60,  0,  0,  0,  0,
12 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  78, 0, 122,  0,  0,  0,  0,
13 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  60, 0,  82,  0,  0,  0,  0,
14 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 122, 0, 222,  0,  0,  0,  0,
15 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  82, 0, 260,  0,  0,  0,  0,
16 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 222, 0, 232,  0,  0,  0,  0,
17 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 260, 0, 114,  0,  0,  0,  0,
18 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 232, 0,  46,  0,  0,  0,  0,
19 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0, 114, 0,  44,  0,  0,  0,  0,
20 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  46, 0,  78,  0,  0,  0,  0,
21 | 0, 0, 0, 0, 0, 0, 0,  0, 0, 0, 0,  0,  0,  44, 0, 252,  0,  0,  0,  0,
		

Crossrefs

Cf. A075677, A086893, A372283, A372358, A372360 (binary weights), A372446 (column 14).

Cf. also A372359.

Programs

PARI

up_to = 105;
R(n) = { n = 1+3*n; n>>valuation(n, 2); };
A372283sq(n,k) = if(1==n,2*k-1,R(A372283sq(n-1,k)));
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);
A372361sq(n,k) = A372358(A372283sq(n,k));
A372361list(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] = A372361sq((a-(col-1)),col))); (v); };
v372361 = A372361list(up_to);
A372361(n) = v372361[n];