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A002705
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Sets with a congruence property.
(Formerly M3673 N1497)
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6
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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)
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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FORMULA
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See Maple code!
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MAPLE
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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:
nloc := 2+4*n ;
Q(nloc, 2) ;
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MATHEMATICA
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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[4 n + 2, 2];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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