OFFSET
1,2
REFERENCES
V. S. Shevelev, On number of solutions of congruence Sum{i=1,...,s}x_i==r(modk), Izvestia Vuzov of the North-Caucasus region, Nature sciences, 2 (1997), 25-37 (in Russian).
FORMULA
a(n) = ((n-1)!/2)*Sum_{d|n} ( -1)^(n+d)*mu(n/d)*C(2d,d), where mu(n) is the Mobius function A008683.
EXAMPLE
If n=2, then we have the congruence x_1 + x_2 == 1 (mod 4), x_i is in {0,1,2,3}. Here we have 4 solutions: (0,1), (1,0), (2,3), (3,2); therefore a(2)=4.
PROG
(PARI) a(n) = ((n-1)!/2) * sumdiv(n, d, ( -1)^(n+d) * moebius(n/d) * binomial(2*d, d) );
vector(33, n, a(n)) \\ Joerg Arndt, Sep 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Mar 26 2010, Apr 09 2010, Jun 29 2010
EXTENSIONS
a(6) corrected and more terms from Joerg Arndt, Sep 05 2018
STATUS
approved