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A002705 Sets with a congruence property.
(Formerly M3673 N1497)
6
0, 4, 40, 468, 5828, 76260, 1032444, 14316584, 202116108, 2893451652, 41886157564, 611902123284, 9007199254740, 133439988963012, 1987795697598012, 29752813022112180, 447193795726343004, 6746237832670921768, 102105221251235572188 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The values for k=1, Q(n,1) in table 1 on page 315 for n = 3,5,7,9,... are 0, 2, 6, 18, 62, 210, 728, 2570, 9198, 33288, 121574, 447394, 1657008, 6170930, 23091222, 86767016, 327235610, 1238188770, 4698767640 ... (see A262590), - R. J. Mathar, Oct 21 2015

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=0..18.

Rosa, Alexander; Znam, Stefan, 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.]

Rosa, Alexander; Znam, Stefan, A remark on a combinatorial problem (Russian with English summary), Mat.-Fyz. Casopis Sloven. Akad. Vied 15 1965 313-316. [Annotated scanned copy] See Table 2.

FORMULA

See Maple code!

MAPLE

p := proc(r, s, k)

    option remember;

    if r = 0 then

        1;

    elif r < 0 then

        0;

    elif s < 0 then

        0;

    elif igcd(s, 2*k+1) > 1 then

        procname(r, s-1, k) ;

    else

        procname(r, s-1, k)+procname(r-s, s-1, k) ;

    end if;

end proc:

Q := proc(n, k)

    local q, knrat, alpha, m ;

    q := 0 ;

    knrat := (2*k*n^2+n^2+k^2)/4/k ;

    if type(knrat, 'integer') then

        for alpha from 0 to knrat do

            m := 2*n+n/k ;

            if modp(2*alpha, m) = modp(knrat, m) then

                q := q+p(alpha, n+(n-k)/2/k, k) ;

            end if;

        end do:

    end if;

    q ;

end proc:

A002705 := proc(n)

    nloc := 2+4*n ;

    Q(nloc, 2) ;

end proc: # R. J. Mathar, Oct 21 2015

CROSSREFS

Cf. A002703, A002704, A262585, A262590.

Sequence in context: A114468 A264112 A304447 * A235372 A034385 A249927

Adjacent sequences:  A002702 A002703 A002704 * A002706 A002707 A002708

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified August 20 20:50 EDT 2019. Contains 326155 sequences. (Running on oeis4.)