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A372361
Array read by upward antidiagonals: A(n, k) = A372358(A372283(n, k)), n,k >= 1.
5
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
1,10
EXAMPLE
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,
PROG
(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];
CROSSREFS
Cf. A075677, A086893, A372283, A372358, A372360 (binary weights), A372446 (column 14).
Cf. also A372359.
Sequence in context: A358622 A336563 A048146 * A334045 A028973 A066503
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 01 2024
STATUS
approved