A360099 To get A(n,k), replace 0's in the binary expansion of n with (-1) and interpret the result in base k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
0, 0, 1, 0, 1, -1, 0, 1, 0, 1, 0, 1, 1, 2, -1, 0, 1, 2, 3, -1, 1, 0, 1, 3, 4, 1, 1, -1, 0, 1, 4, 5, 5, 3, 1, 1, 0, 1, 5, 6, 11, 7, 5, 3, -1, 0, 1, 6, 7, 19, 13, 11, 7, -2, 1, 0, 1, 7, 8, 29, 21, 19, 13, 1, 0, -1, 0, 1, 8, 9, 41, 31, 29, 21, 14, 3, 0, 1, 0, 1, 9, 10, 55, 43, 41, 31, 43, 16, 5, 2, -1
Offset: 0
Examples
Square array A(n,k) begins: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... -1, -1, 1, 5, 11, 19, 29, 41, 55, 71, 89, ... 1, 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, ... -1, 1, 5, 11, 19, 29, 41, 55, 71, 89, 109, ... 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, ... -1, -2, 1, 14, 43, 94, 173, 286, 439, 638, 889, ... 1, 0, 3, 16, 45, 96, 175, 288, 441, 640, 891, ... -1, 0, 5, 20, 51, 104, 185, 300, 455, 656, 909, ...
Links
- Alois P. Heinz, Antidiagonals n = 0..200, flattened
Crossrefs
Programs
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Maple
A:= proc(n, k) option remember; local m; `if`(n=0, 0, k*A(iquo(n, 2, 'm'), k)+2*m-1) end: seq(seq(A(n, d-n), n=0..d), d=0..12); # second Maple program: A:= (n, k)-> (l-> add((2*l[i]-1)*k^(i-1), i=1..nops(l)))(Bits[Split](n)): seq(seq(A(n, d-n), n=0..d), d=0..12);
Comments