OFFSET
0,3
COMMENTS
Number of starting configurations of Nim such that the 1st player wins, and the configurations are in the form {x_1, x_2, ..., x_n}, where x_i is the number of pieces on i-th stack (x_i>=0), and the sum of all pieces is n.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
C. L. Bouton, Nim, A Game with a Complete Mathematical Theory, Annals of Mathematics, Second Series, vol. 3 (1/4), 1902, 35-39.
FORMULA
a(n) = A088218(n) if n is odd.
EXAMPLE
For n=2 the a(2)=2 solutions are: {0,2}, {2,0}.
For n=3 the a(3)=10 solutions are: {0,0,3}, {0,1,2}, {0,2,1}, {0,3,0}, {1,0,2}, {1,1,1}, {1,2,0}, {2,0,1}, {2,1,0}, {3,0,0}.
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, signum(t),
add(b(n-j, i-1, Bits[Xor](j, t)), j=`if`(i=1, n, 0..n)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..32); # Alois P. Heinz, May 15 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Anna Ledworowska, May 15 2024
STATUS
approved