OFFSET
1,3
FORMULA
All partitions of size n: if GCD is not 1, skip; else: fill the partition with zeros to get k numbers; count occurrences of each number (e.g.: 2 2 1 0 0 0 becomes 2 1 3); compute multinomial of k over these digits (e.g. 2 1 3 becomes 6!/(2!*1!*3!) = 60); sum.
EXAMPLE
Table array begins:
1 1 1 1 1
2 3 5 7 11
3 6 13 22 40
4 10 26 51 103
5 15 45 100 221
...
a(3,2) = 6 because you can take each color once, or mix two colors.
MATHEMATICA
max = 10; col[k_] := Accumulate[ Table[ Sum[ MoebiusMu[n/d]*Product[d+j, {j, 1, k}]/k!, {d, Divisors[n]}], {n, 1, max}]]; t = Table[col[k], {k, 0, max-1}] // Transpose; Flatten[ Table[ t[[n-k+1, k]], {n, 1, max}, {k, 1, n}]] (* Jean-François Alcover, Dec 26 2012 *)
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
Name edited by Michel Marcus, Aug 11 2024
STATUS
approved