This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A048600 #18 Aug 11 2024 10:35:19
%S A048600 1,1,2,1,3,3,1,5,6,4,1,7,13,10,5,1,11,22,26,15,6,1,13,40,51,45,21,7,1,
%T A048600 19,55,103,100,71,28,8,1,23,88,161,221,176,105,36,9,1,29,118,277,386,
%U A048600 422,287,148,45,10
%N A048600 Array a(n,k) = number of colors that can be produced by n units of paint from k primary colors, read by descending antidiagonals.
%F A048600 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.
%e A048600 Table array begins:
%e A048600 1 1 1 1 1
%e A048600 2 3 5 7 11
%e A048600 3 6 13 22 40
%e A048600 4 10 26 51 103
%e A048600 5 15 45 100 221
%e A048600 ...
%e A048600 a(3,2) = 6 because you can take each color once, or mix two colors.
%t A048600 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 *)
%Y A048600 Cf. A005728 (row 2), A048134 (row 3). Cf. A048240, A048241.
%K A048600 easy,nice,nonn,tabl
%O A048600 1,3
%A A048600 _Jurjen N.E. Bos_
%E A048600 Name edited by _Michel Marcus_, Aug 11 2024