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A032801 Number of unordered sets a,b,c,d of distinct integers from 1..n such that a+b+c+d=0 (mod n). 0
0, 0, 0, 0, 1, 3, 5, 9, 14, 22, 30, 42, 55, 73, 91, 115, 140, 172, 204, 244, 285, 335, 385, 445, 506, 578, 650, 734, 819, 917, 1015, 1127, 1240, 1368, 1496, 1640, 1785, 1947, 2109, 2289, 2470, 2670, 2870, 3090 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

REFERENCES

E. V. McLaughlin, Numbers of factorizations in non-unique factorial domains, Senior Thesis, Allegeny College, Meadville, PA, April 2004.

LINKS

Table of n, a(n) for n=1..44.

E. S. Barnes, The construction of perfect and extreme forms I, Acta Arith., 5 (1959), p. 65.

FORMULA

G.f.: (x^4/4)*(1/(1 - x)^4 + 1/(1 - x^2)^2 - 2/(1 - x^4)) (conjectured). -  Herbert Kociemba, Oct 22 2016

a(n) = (-6*(4+2*(-1)^n+(-i)^n+i^n)+(25+3*(-1)^n)*n-12*n^2+2*n^3)/48 (conjectured) - Colin Barker, Oct 23 2016

MAPLE

f := n-> if n mod 2 <> 0 then (n-1)*(n-2)*(n-3)/24 elif n mod 4 = 0 then (n-4)*(n^2-2*n+6)/24 else (n-2)*(n^2-4*n+6)/24; fi;

CROSSREFS

Cf. A001399, A001400.

Sequence in context: A053618 A268345 A267047 * A033818 A320598 A227567

Adjacent sequences:  A032798 A032799 A032800 * A032802 A032803 A032804

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Offset changed by David A. Corneth, Oct 23 2016

STATUS

approved

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Last modified April 19 21:01 EDT 2019. Contains 322291 sequences. (Running on oeis4.)