A002703 - OEIS

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A002703

Sets with a congruence property.
(Formerly M1598 N0624)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,4

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

Table of n, a(n) for n=3..39.

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.

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 *)

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.

Sequence in context: A238410 A256482 A106353 * A230978 A112853 A176752

Adjacent sequences: A002700 A002701 A002702 * A002704 A002705 A002706

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved