|
|
A050314
|
|
Triangle: a(n,k) = number of partitions of n whose xor-sum is k.
|
|
10
|
|
|
1, 0, 1, 1, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 3, 0, 2, 0, 2, 4, 0, 3, 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 5, 6, 0, 5, 0, 4, 0, 6, 0, 1, 0, 8, 0, 6, 0, 8, 0, 6, 0, 2, 10, 0, 9, 0, 11, 0, 8, 0, 2, 0, 2, 0, 11, 0, 14, 0, 12, 0, 12, 0, 2, 0, 5, 16, 0, 18, 0, 15, 0, 16, 0, 4, 0, 6, 0, 2, 0, 23, 0, 20, 0, 20, 0, 19, 0, 8, 0, 6, 0, 5
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle: a(n,k) begins:
1;
0, 1;
1, 0, 1;
0, 1, 0, 2;
2, 0, 2, 0, 1;
0, 3, 0, 2, 0, 2;
4, 0, 3, 0, 2, 0, 2;
0, 4, 0, 4, 0, 2, 0, 5;
6, 0, 5, 0, 4, 0, 6, 0, 1;
0, 8, 0, 6, 0, 8, 0, 6, 0, 2;
10, 0, 9, 0, 11, 0, 8, 0, 2, 0, 2;
0, 11, 0, 14, 0, 12, 0, 12, 0, 2, 0, 5;
16, 0, 18, 0, 15, 0, 16, 0, 4, 0, 6, 0, 2;
...
|
|
MAPLE
|
with(Bits):
b:= proc(n, i, k) option remember; `if`(n=0, x^k, `if`(i<1, 0,
add(b(n-i*j, i-1, `if`(j::even, k, Xor(i, k))), j=0..n/i)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n$2, 0)):
|
|
MATHEMATICA
|
b[n_, i_, k_] := b[n, i, k] = If[n==0, x^k, If[i<1, 0, Sum[b[n-i*j, i-1, If[EvenQ[j], k, BitXor[i, k]]], {j, 0, n/i}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, n, 0]]; Table[T[n], {n, 0, 20}] // Flatten (* Jean-François Alcover, Jan 24 2016, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|