OFFSET
3,1
LINKS
Alexander Rosa and Štefan Znám, A combinatorial problem in the theory of congruences. (Russian), Mat.-Fys. Casopis Sloven. Akad. Vied 15 1965 49-59. [Annotated scanned copy] This is Q(n) in Table 3.
FORMULA
See Maple code! - N. J. A. Sloane, Oct 21 2015
MAPLE
A178666 := proc(r, s)
product( (1+x^(2*i+1)), i=0..floor((s-1)/2)) ;
expand(%) ;
coeftayl(%, x=0, r) ;
end proc:
kstart := proc(n, m)
ceil(binomial(n+1, 2)/m) ;
end proc:
kend := proc(n, m)
floor(binomial(3*n+1, 2)/3/m) ;
end proc:
A262568 := proc(n)
local s, m, Q , vi, k;
s := 2*n-1 ;
m := 2*n+1 ;
Q := 0 ;
for k from kstart(n, m) to kend(n, m) do
vi := m*k-binomial(n+1, 2) ;
Q := Q+A178666(vi, s) ;
end do:
Q ;
end proc: # R. J. Mathar, Oct 21 2015
MATHEMATICA
A178666[r_, s_] := SeriesCoefficient[Product[(1 + x^(2i+1)), {i, 0, Floor[ (s - 1)/2]}], {x, 0, r}];
kstart [n_, m_] := Ceiling[Binomial[n+1, 2]/m];
kend[n_, m_] := Floor[Binomial[3n+1, 2]/3/m];
a[n_] := Module[{s = 2n-1, m = 2n+1, Q=0, vi, k}, For[k = kstart[n, m], k <= kend[n, m], k++, vi = m k - Binomial[n+1, 2]; Q += A178666[vi, s]]; Q];
a /@ Range[3, 38] (* Jean-François Alcover, Mar 24 2020, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2015
EXTENSIONS
More terms from R. J. Mathar, Oct 21 2015
Missing a(16) inserted by Sean A. Irvine, Oct 23 2015
STATUS
approved