A039826 Largest coefficient in expansion of Product_{i=1..n} (1 + q^i + q^(2i)).

1, 2, 3, 7, 15, 36, 87, 217, 549, 1423, 3735, 9911, 26513, 71581, 194681, 532481, 1464029, 4045117, 11225159, 31268577, 87404465, 245101771, 689323849, 1943817227, 5494808425, 15568077235, 44200775239, 125739619467, 358347118257, 1022994133467, 2925044957099, 8376049588815, 24018964753341

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..2106 (terms < 10^1000)
• Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]

Crossrefs

Cf. A039827.

Programs

Mathematica

nmax = 28; d = {1}; a1 = {};
Do[
  n0s = Table[0, {n}];
  d = Join[d, n0s, n0s] + Join[n0s, d, n0s] + Join[n0s, n0s, d];
  AppendTo[a1, Last[Union[d]]];
  , {n, nmax}];
a1 (* Ray Chandler, Mar 26 2014 *)

PARI

a(n)=vecmax(Vec(prod(k=1,n,1+x^k+x^(2*k))));
vector(50,n,a(n)) \\ Joerg Arndt, Jan 31 2024

Formula

a(n) ~ 3^(n+1) / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 11 2018