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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
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)):
seq(T(n), n=0..20); # Alois P. Heinz, Dec 01 2015
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
a(2n,0) = A048833(n). a(2n+1,1) = A050316(n). a(n,n) = A050315(n).
Row sums give A000041.
a(4n,2n) gives A370874.
Sequence in context: A073464 A142242 A362634 * A316344 A122157 A080378
KEYWORD
nonn,tabl,base,look
AUTHOR
Christian G. Bower, Sep 15 1999
STATUS
approved