A002703 Sets with a congruence property.

0, 0, 0, 2, 6, 14, 24, 46, 88, 162, 300, 562, 1056, 1982, 3742, 7082, 13438, 25574, 48768, 93198, 178480, 342392, 657918, 1266202, 2440318, 4709374, 9099504, 17602322, 34087010, 66076414, 128207976, 248983550, 483939976, 941362694, 1832519262, 3569842946, 6958934352

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is the sequence k(n) in Table 3 of the first 1965 paper. - N. J. A. Sloane, Oct 20 2015

See English summary at the end of the first 1965 paper, which is repeated in the Zentralblatt review. - Jonathan Sondow, Nov 02 2013

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alexander Rosa and Štefan Znám, A combinatorial problem in the theory of congruences (Russian with English summary), Mat.-Fys. Casopis Sloven. Akad. Vied 15 (1965) 49-59. [Annotated scanned copy.] This is the sequence k(n) in Table 3. Tables 1 and 2 are A053632 and A178666 respectively.
• Alexander Rosa and Štefan Znám, A remark on a combinatorial problem (Russian with English summary), Mat.-Fyz. Casopis Sloven. Akad. Vied 15 (1965) 313-316. [Annotated scanned copy]
• Zentralblatt, Review of Rosa and Znám, A combinatorial problem in the theory of congruences.

Crossrefs

Cf. A002704, A002705.

See A262567, A262568, A262569 for other versions.

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

Programs

Maple

A002703 := proc(n)
    A262568(n)-2 ;
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];
A262568[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[n_] := A262568[n] - 2;
a /@ Range[3, 39] (* Jean-François Alcover, Mar 24 2020, after R. J. Mathar in A262568 *)

Extensions

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