OFFSET
1,2
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-4) +a(n-5) +a(n-6) -4*a(n-7) +4*a(n-9) -a(n-10) -a(n-11) -a(n-12) -a(n-13) +4*a(n-14) -4*a(n-16) +a(n-17) +a(n-18) +2*a(n-19) -a(n-20) -5*a(n-21) +5*a(n-22) +a(n-23) -2*a(n-24) -a(n-25) -a(n-26) +4*a(n-27) -4*a(n-29) +a(n-30) +a(n-31) +a(n-32) +a(n-33) -4*a(n-34) +4*a(n-36) -a(n-37) -a(n-38) -2*a(n-39) +2*a(n-40) +2*a(n-41) -3*a(n-42) +a(n-43).
EXAMPLE
Some solutions for n=8:
..2....3....2....2....2....2....3....3....2....2....2....2....4....5....3....2
..2....3....2....2....3....5....3....4....2....3....2....2....4....5....3....3
..2....3....3....2....3....6....4....4....3....4....2....3....4....5....3....3
..3....3....3....2....3....6....4....4....3....4....2....3....5....5....3....3
..3....3....4....2....6....6....4....5....4....4....2....4....6....6....3....3
..3....3....5....2....6....6....4....6....4....4....2....5....6....6....5....3
..4....3....6....4....6....6....4....6....5....5....2....5....6....6....6....3
..4....4....6....5....6....6....5....6....6....5....5....5....6....6....6....3
MAPLE
S6:= combinat:-powerset({$2..6}):
f:= proc(n) local s, t, G, S, i, j, T;
t:= 0:
for S in S6 do
G:= coeff(mul(add(x^i*y^(i*j), i=0..n), j=S), x, n);
T:= select(s -> S = select(k -> s mod k <> 0, {$2..6}), [$2*n..6*n]);
t:= t + add(coeff(G, y, s), s= T);
od;
t
end proc:
map(f, [$1..50]); # Robert Israel, Nov 23 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 29 2012
STATUS
approved