A048240 Number of new colors that can be mixed with n units of yellow, blue, red.

1, 3, 3, 7, 9, 18, 15, 33, 30, 45, 42, 75, 54, 102, 81, 108, 108, 168, 117, 207, 156, 210, 195, 297, 204, 330, 270, 351, 306, 462, 300, 525, 408, 510, 456, 612, 450, 738, 567, 708, 600, 900, 594, 987, 750, 900, 825, 1173, 792, 1239, 930, 1200

Offset: 0

Author

Jurjen N.E. Bos, N. J. A. Sloane, Robin Trew (trew(AT)hcs.harvard.edu)

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Vadym Kurylenko, Thin Simplices via Modular Arithmetic, arXiv:2404.03975 [math.CO], 2024. See p. 33.

Crossrefs

Cf. A048134, A048241.

A032125(n) = a(2^n).

Cf. A000217, A008683, A000741, A023023.

Programs

Maple

A048240 := proc(n) local ans, i, j, k; ans := 0; for i from n by -1 to 0 do for j from n by -1 to 0 do k := n - i - j; if 0 <= k and k <= n and gcd(gcd(i, j), k) = 1 then ans := ans + 1; fi; od; od; RETURN(ans); end;

Mathematica

a[n_] := Sum[ MoebiusMu[n/d]*(d+1)*(d+2)/2, {d, Divisors[n]}]; a[0] = 1; Table[a[n], {n, 0, 51}] (* Jean-François Alcover, Jun 14 2012, after Vladeta Jovovic *)

Formula

a(n) = number of triples (i, j, k) with i+j+k = n and gcd(i, j, k) = 1.

a(n) = Sum_{d|n} mu(n/d)*(d+1)*(d+2)/2. G.f.: Sum_{k>0} mu(k)/(1-x^k)^3. - Vladeta Jovovic, Dec 22 2002