A262568 a(n) = A002703(n) + 2.

2, 2, 2, 4, 8, 16, 26, 48, 90, 164, 302, 564, 1058, 1984, 3744, 7084, 13440, 25576, 48770, 93200, 178482, 342394, 657920, 1266204, 2440320, 4709376, 9099506, 17602324, 34087012, 66076416, 128207978, 248983552, 483939978, 941362696, 1832519264, 3569842948

Offset: 3

Author

N. J. A. Sloane, Oct 20 2015

Keywords

• nonn

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.

Crossrefs

Cf. A002703, A262567, A262569.

Tables 1 and 2 of the first Rosa-Znám 1965 paper are A053632 and A178666 respectively.

Programs

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 *)

Formula

See Maple code! - N. J. A. Sloane, Oct 21 2015

Extensions

More terms from R. J. Mathar, Oct 21 2015

Missing a(16) inserted by Sean A. Irvine, Oct 23 2015