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%I #8 Apr 29 2024 09:07:07
%S 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,
%T 0,0,16777216,0,0,2,0,0,0,0,0,0,0,8,4,0,0,0,0,0,0,0,896,0,6,0,0,0,0,0,
%U 0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,6144,0,2,0,0,0,0,0,0,0,0,0,16777216,0,56,4
%N Array read by upward antidiagonals: A(n, k) = A372352(A372282(n, k)), n,k >= 1.
%C Zeros occur in the same locations where 1's occur in array A372287.
%e Array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13
%e ---+---------------------------------------------------------------------------
%e 1 | 0, 0, 0, 2, 4, 6, 0, 2, 4, 6, 0, 2, 4,
%e 2 | 0, 0, 0, 24, 32, 16, 0, 8, 0, 32, 0, 56, 96,
%e 3 | 0, 0, 0, 256, 6144, 0, 0, 896, 0, 6144, 0, 0, 8192,
%e 4 | 0, 0, 0, 0, 16777216, 0, 0, 0, 0, 16777216, 0, 0, 402653184,
%e 5 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72057594037927936,
%e 6 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
%o (PARI)
%o up_to = 91;
%o A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
%o A372352(n) = { my(k); for(i=1,oo,k=A086893(i); if(k>n, return(n-A086893(i-1)))); };
%o A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372353sq(n,k) = A372352(A372282sq(n,k));
%o A372353list(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] = A372353sq((a-(col-1)),col))); (v); };
%o v372353 = A372353list(up_to);
%o A372353(n) = v372353[n];
%Y Cf. A086893, A096773, A372352, A372282, A372287.
%Y Cf. also A372285 and A372355 (columnwise first differences).
%K nonn,tabl
%O 1,10
%A _Antti Karttunen_, Apr 29 2024
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