This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372357 #6 Apr 30 2024 17:05:28
%S A372357 0,0,2,0,0,0,0,0,0,-1,0,0,0,-1,1,0,0,0,3,-1,-1,0,0,0,2,-1,3,2,0,0,0,0,
%T A372357 3,2,0,-1,0,0,0,0,2,0,0,-2,3,0,0,0,0,0,0,0,5,2,3,0,0,0,0,0,0,0,2,0,-1,
%U A372357 0,0,0,0,0,0,0,0,0,0,-1,0,-2,0,0,0,0,0,0,0,0,0,3,0,5,-2,0,0,0,0,0,0,0,0,0,2,0,2,3,-1
%N A372357 Array read by upward antidiagonals: A(n, k) = A372356(1+n,k)-2*A372356(n,k), n,k >= 1.
%e A372357 Array begins:
%e A372357 n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A372357 ---+-----------------------------------------------------------------------------
%e A372357 1 | 0, 2, 0, -1, 1, -1, 2, -1, 3, 3, 0, -2, -2, -1, -1, -1, 2, 5, 1, 1, 1,
%e A372357 2 | 0, 0, 0, -1, -1, 3, 0, -2, 2, -1, 0, 5, 3, 1, -1, -2, -2, 2, -1, 0, -1,
%e A372357 3 | 0, 0, 0, 3, -1, 2, 0, 5, 0, -1, 0, 2, -1, -1, 3, 1, 3, 0, -1, -2, -2,
%e A372357 4 | 0, 0, 0, 2, 3, 0, 0, 2, 0, 3, 0, 0, -1, -2, 2, -1, -1, 0, 3, 4, 1,
%e A372357 5 | 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 3, 1, 0, 2, -1, 0, 2, -2, -1,
%e A372357 6 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, -1, 3, 0, 0, 3, 2,
%e A372357 7 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 2, 0, 0, -1, -1,
%e A372357 8 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, -1,
%e A372357 9 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 3, 1,
%e A372357 10 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -2,
%e A372357 11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 2,
%e A372357 12 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1,
%e A372357 13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -2,
%e A372357 14 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 1,
%e A372357 15 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, -1,
%e A372357 16 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 3,
%e A372357 17 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, -2,
%e A372357 18 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1,
%e A372357 19 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0,
%e A372357 20 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2,
%e A372357 21 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 2,
%o A372357 (PARI)
%o A372357 up_to = 105;
%o A372357 A000523(n) = logint(n,2);
%o A372357 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372357 A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372357 A372356sq(n,k) = { my(x=A372282sq(n,k)); (A000523(A371094(x))-A000523(x)); };
%o A372357 A372357sq(n,k) = (A372356sq(1+n,k)-2*A372356sq(n,k));
%o A372357 A372357sq(n,k) = { my(x=A372282sq(n,k), y=A371094(x), z=A371094(y), xl=A000523(x), yl=A000523(y), zl=A000523(z)); ((zl-yl) - 2*(yl-xl)); };
%o A372357 A372357sq(n,k) = { my(x=A372282sq(n,k), y=A371094(x), z=A371094(y), xl=A000523(x), yl=A000523(y), zl=A000523(z)); (zl - 3*yl + 2*xl); };
%o A372357 A372357list(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] = A372357sq((a-(col-1)),col))); (v); };
%o A372357 v372357 = A372357list(up_to);
%o A372357 A372357(n) = v372357[n];
%Y A372357 Cf. A000523, A371094, A372282, A372354, A372356.
%K A372357 sign,tabl
%O A372357 1,3
%A A372357 _Antti Karttunen_, Apr 30 2024