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

0,2

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.

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

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 *)

Crossrefs

Cf. A048134, A048241.

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

Cf. A000217, A008683, A000741, A023023.

Sequence in context: A034411 A258289 A066983 * A122012 A185306 A379914

Adjacent sequences: A048237 A048238 A048239 * A048241 A048242 A048243

Keyword

nonn,easy

Author

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

Status

approved