OFFSET
1,5
COMMENTS
See A245558 for identification of other sequences occurring in this triangle.
LINKS
A. Elashvili and M. Jibladze, Hermite reciprocity for the regular representations of cyclic groups, Indag. Math. (N.S.) 9 (1998), no. 2, 233-238; MR1691428 (2000c:13006).
A. Elashvili, M. Jibladze, and D. Pataraia, Combinatorics of necklaces and "Hermite reciprocity", J. Algebraic Combin. 10 (1999), no. 2, 173-188; MR1719140 (2000j:05009). See p. 174.
J. E. Iglesias, Enumeration of closest-packings by the space group: a simple approach, Z. Krist. 221 (2006) 237-245, eq. (5).
EXAMPLE
Triangle begins:
1,
1, 1,
1, 2, 3,
1, 2, 5, 8,
1, 3, 7, 14, 25,
1, 3, 9, 20, 42, 75,
1, 4, 12, 30, 66, 132, 245,
1, 4, 15, 40, 99, 212, 429, 800,
1, 5, 18, 55, 143, 333, 715, 1430, 2700,
1, 5, 22, 70, 200, 497, 1144, 2424, 4862, 9225,
1, 6, 26, 91, 273, 728, 1768, 3978, 8398, 16796, 32065,
1, 6, 30, 112, 364, 1026, 2652, 6288, 13995, 29372, 58786, 112632
...
MAPLE
A245559 := proc(p, q)
local d;
a := 0 ;
for d from 1 to max(p, q) do
if modp(p, d)=0 and modp(q, d)=0 then
a := a+numtheory[mobius](d)*(binomial((p+q)/d, p/d)) ;
end if ;
end do:
a/(p+q) ;
end proc:
seq(seq( A245559(p, q), q=1..p), p=1..12) ; # R. J. Mathar, Apr 15 2024
MATHEMATICA
A245559[p_, q_] := Module[{d, a = 0}, For[d = 1, d <= Max[p, q], d++, If[Mod[p, d] == 0 && Mod[q, d] == 0, a = a + MoebiusMu[d]*Binomial[ (p+q)/d, p/d]]]; a/(p+q)];
Table[Table[A245559[p, q], {q, 1, p}], {p, 1, 12}] // Flatten (* Jean-François Alcover, May 17 2024, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 07 2014
STATUS
approved