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A002704 Sets with a congruence property.
(Formerly M2146 N0855)
6
2, 26, 938, 42800, 2130458, 111557594, 6041272682, 335089258634, 18922687509962, 1083572842675610, 62744027461625648, 3666433604712457466, 215879610645469496234, 12792865816027823374874, 762278349313657804740842, 45638342462133835019322554 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..15.

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 3.

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:

A002704 := proc(n)

    nloc := 3+6*n ;

    Q(nloc, 3) ;

end proc:

seq(A002704(n), n=0..15) ; # R. J. Mathar, Oct 21 2015

CROSSREFS

Cf. A002703, A002705, A262570, A262583, A262584.

Sequence in context: A059516 A210672 A173103 * A015215 A158120 A209916

Adjacent sequences:  A002701 A002702 A002703 * A002705 A002706 A002707

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 July 1 18:11 EDT 2016. Contains 274322 sequences.