A039827 Number of different coefficient values in expansion of Product (1+q^i+q^(2i)), i=1 to n.

1, 2, 3, 6, 11, 19, 26, 34, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, 1224, 1274

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A039826.

Programs

Mathematica

nmax = 50; d = {1}; a1 = {};
Do[
  n0s = Table[0, {n}];
  d = Join[d, n0s, n0s] + Join[n0s, d, n0s] + Join[n0s, n0s, d];
  AppendTo[a1, Length[Union[d]]];
  , {n, nmax}];
a1 (* Ray Chandler, Mar 26 2014 *)

Formula

Conjectures from Chai Wah Wu, Jun 22 2016: (Start)

a(n) = n*(n+1)/2 - 1 for n >= 9.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 11.

G.f.: x*(-x^10 + 2*x^9 - x^8 - 2*x^7 + 4*x^6 - x^5 - 2*x^3 + x - 1)/(x - 1)^3. (End)