A357914 Iterated partial sums of the Moebius mu function, square array read by ascending antidiagonals.
1, 1, -1, 1, 0, -1, 1, 1, -1, 0, 1, 2, 0, -1, -1, 1, 3, 2, -1, -2, 1, 1, 4, 5, 1, -3, -1, -1, 1, 5, 9, 6, -2, -4, -2, 0, 1, 6, 14, 15, 4, -6, -6, -2, 0, 1, 7, 20, 29, 19, -2, -12, -8, -2, 1, 1, 8, 27, 49, 48, 17, -14, -20, -10, -1, -1, 1, 9, 35, 76, 97, 65, 3, -34, -30, -11, -2, 0
Offset: 1
Examples
Array begins: n\k| 1 2 3 4 5 6 7 8 9 10 ... ---+------------------------------------------------------- 1 | 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, ... = A008683 2 | 1, 0, -1, -1, -2, -1, -2, -2, -2, -1, ... = A002321 3 | 1, 1, 0, -1, -3, -4, -6, -8, -10, -11, ... = A091555 4 | 1, 2, 2, 1, -2, -6, -12, -20, -30, -41, ... 5 | 1, 3, 5, 6, 4, -2, -14, -34, -64, -105, ... 6 | 1, 4, 9, 15, 19, 17, 3, -31, -95, -200, ... 7 | 1, 5, 14, 29, 48, 65, 68, 37, -58, -258, ... 8 | 1, 6, 20, 49, 97, 162, 230, 267, 209, -49, ... 9 | 1, 7, 27, 76, 173, 335, 565, 832, 1041, 992, ... 10 | 1, 8, 35, 111, 284, 619, 1184, 2016, 3057, 4049, ... ...
Crossrefs
Programs
Formula
T(1,k) = A008683(k) for k >= 1; T(n,k) = Sum_{i=1..k} T(n-1,i) for n > 1, k >= 1.