A002704 Number of sets with a congruence property.
2, 26, 938, 42800, 2130458, 111557594, 6041272682, 335089258634, 18922687509962, 1083572842675610, 62744027461625648, 3666433604712457466, 215879610645469496234, 12792865816027823374874, 762278349313657804740842, 45638342462133835019322554
Offset: 0
Keywords
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.]
- 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]. See Table 3 on page 316.
Programs
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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 -
Mathematica
p[r_, s_, k_] := p[r, s, k] = Which[r == 0, 1, r < 0, 0, s < 0, 0, GCD[s, 2 k + 1] > 1, p[r, s - 1, k], True, p[r, s - 1, k] + p[r - s, s - 1, k]]; Q[n_, k_] := Module[{q = 0, knrat, alpha, m}, knrat = (2 k n^2 + n^2 + k^2)/4/k; If[IntegerQ[knrat], For[alpha = 0, alpha <= knrat, alpha++, m = 2 n + n/k; If[Mod[2 alpha, m] == Mod[knrat, m], q += p[alpha, n + (n - k)/2/k, k]]]]; q]; a[n_] := Q[6 n + 3, 3]; a /@ Range[0, 15] (* Jean-François Alcover, Mar 27 2020, after R. J. Mathar *)
Formula
See Maple code!
Extensions
More terms from R. J. Mathar, Oct 21 2015