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A066571 Number of sets of positive integers with arithmetic mean n. 4
1, 3, 9, 31, 117, 479, 2061, 9183, 42021, 196239, 931457, 4480531, 21793257, 107004891, 529656765, 2640160039, 13241371629, 66771501151, 338333343825, 1721768732423, 8796192611917, 45096680384635, 231945566136129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contribution from Franklin T. Adams-Watters, Sep 13 2011 (Start) If we use nonnegative integers instead of positive integers, we get this sequence shifted left (i.e., with offset 0).

The largest number that can be included in set of positive integers with mean n is the triangular number n*(n+1)/2 = A000217(n).

All values are odd. Sets including n are paired with the same set with n removed, with exception of {n}, as the empty set has no average.

(End)

LINKS

Table of n, a(n) for n=1..23.

FORMULA

Sum of coefficient of t^k x^(n*k) in Product_{i=1..n*k} (1+t*x^i) for k <= 2*n-1. - N. J. A. Sloane.

EXAMPLE

a(2) = 3 as there are three sets viz. {2), {1,3), {1,2,3}, the arithmetic mean of whose elements is 2.

a(3) = 9: the nine sets are {3}, {1, 5}, {2, 4}, {1, 2, 6}, {1, 3, 5}, {2, 3, 4}, {1, 2, 3, 6}, {1, 2, 4, 5}, {1, 2, 3, 4, 5}

MAPLE

g := k->expand(mul(1+t*x^i, i=1..k)); A066571 := proc(n) local k; add(coeff(coeff(g(n*k), t, k), x, n*k), k=1..2*n-1); end;

PROG

(Haskell)

a066571 n = f [1..] 1 n 0 where

   f (k:ks) l nl x

     | y > nl  = 0

     | y < nl  = f ks (l + 1) (nl + n) y + f ks l nl x

     | otherwise = if y `mod` l == 0 then 1 else 0

     where y = x + k

-- Reinhard Zumkeller, Feb 13 2013

CROSSREFS

Cf. A066572, A000217.

Cf. A072701, A164283.

Sequence in context: A151036 A073724 A151037 * A087648 A086616 A040027

Adjacent sequences:  A066568 A066569 A066570 * A066572 A066573 A066574

KEYWORD

nonn,nice

AUTHOR

Amarnath Murthy, Dec 19 2001

EXTENSIONS

Corrected and extended by N. J. A. Sloane, Dec 19 2001

More terms from Naohiro Nomoto, Jun 19 2002

More terms from David Wasserman, Sep 10 2002

STATUS

approved

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Last modified March 27 13:47 EDT 2017. Contains 284176 sequences.