cp's OEIS Frontend

A372353 Array read by upward antidiagonals: A(n, k) = A372352(A372282(n, k)), n,k >= 1.

%I A372353 #8 Apr 29 2024 09:07:07
%S A372353 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 A372353 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 A372353 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 A372353 Array read by upward antidiagonals: A(n, k) = A372352(A372282(n, k)), n,k >= 1.
%C A372353 Zeros occur in the same locations where 1's occur in array A372287.
%e A372353 Array begins:
%e A372353 n\k| 1  2  3    4         5   6  7    8  9        10 11  12                 13
%e A372353 ---+---------------------------------------------------------------------------
%e A372353 1  | 0, 0, 0,   2,        4,  6, 0,   2, 4,        6, 0,  2,                 4,
%e A372353 2  | 0, 0, 0,  24,       32, 16, 0,   8, 0,       32, 0, 56,                96,
%e A372353 3  | 0, 0, 0, 256,     6144,  0, 0, 896, 0,     6144, 0,  0,              8192,
%e A372353 4  | 0, 0, 0,   0, 16777216,  0, 0,   0, 0, 16777216, 0,  0,         402653184,
%e A372353 5  | 0, 0, 0,   0,        0,  0, 0,   0, 0,        0, 0,  0, 72057594037927936,
%e A372353 6  | 0, 0, 0,   0,        0,  0, 0,   0, 0,        0, 0,  0,                 0,
%o A372353 (PARI)
%o A372353 up_to = 91;
%o A372353 A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
%o A372353 A372352(n) = { my(k); for(i=1,oo,k=A086893(i); if(k>n, return(n-A086893(i-1)))); };
%o A372353 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372353 A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372353 A372353sq(n,k) = A372352(A372282sq(n,k));
%o A372353 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 A372353 v372353 = A372353list(up_to);
%o A372353 A372353(n) = v372353[n];
%Y A372353 Cf. A086893, A096773, A372352, A372282, A372287.
%Y A372353 Cf. also A372285 and A372355 (columnwise first differences).
%K A372353 nonn,tabl
%O A372353 1,10
%A A372353 _Antti Karttunen_, Apr 29 2024