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A039826
Largest coefficient in expansion of Product_{i=1..n} (1 + q^i + q^(2i)).
3
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
1,2
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]
FORMULA
a(n) ~ 3^(n+1) / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 11 2018
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 *)
PROG
(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
CROSSREFS
Cf. A039827.
Sequence in context: A052321 A114584 A328779 * A221547 A289471 A289470
KEYWORD
nonn
STATUS
approved