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

3,1

Links

Table of n, a(n) for n=3..38.

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

Cf. A002703, A262567, A262569.

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

Sequence in context: A099768 A285636 A102831 * A183388 A274076 A160179

Adjacent sequences: A262565 A262566 A262567 * A262569 A262570 A262571

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