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A007785 Number of sets of positive integers <= n^2 whose sum is (n^3 + n)/2. 3
1, 1, 2, 17, 306, 10828, 654857, 63019177, 9183937890, 1953896126383, 589909767142505, 247074213707554144, 140902072248206260266, 107704589610917073318533, 108877374411946899963718973, 143864444783939220165210185294, 245934054410000090878614435736720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..40 (terms n = 1..18 from Sean A. Irvine)

EXAMPLE

a(2) = 2: {1,4}, {2,3}.

a(3) = 17: {6,9}, {7,8}, {1,5,9}, {1,6,8}, {2,4,9}, {2,5,8}, {2,6,7}, {3,4,8}, {3,5,7}, {4,5,6}, {1,2,3,9}, {1,2,4,8}, {1,2,5,7}, {1,3,4,7}, {1,3,5,6}, {2,3,4,6}, {1,2,3,4,5}.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i*(i+1)/2<n, 0,

      b(n, i-1) +`if`(i>n, 0, b(n-i, min(n-i, i-1)))))

    end:

a:= n-> (s-> b(n*(1+s)/2, s))(n^2):

seq(a(n), n=0..16);  # Alois P. Heinz, Nov 02 2018

CROSSREFS

Cf. A052456.

Sequence in context: A078367 A090306 A304857 * A201785 A204249 A242368

Adjacent sequences:  A007782 A007783 A007784 * A007786 A007787 A007788

KEYWORD

nonn

AUTHOR

Hidetoshi MINO [ mino(AT)hep.esb.yamanashi.ac.jp, mino(AT)mino.scri.fsu.edu ]

EXTENSIONS

Corrected and extended by David W. Wilson

a(12) corrected and more terms from Sean A. Irvine, Jan 27 2018

a(0)=1 prepended by Alois P. Heinz, Nov 02 2018

STATUS

approved

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Last modified January 17 10:21 EST 2019. Contains 319218 sequences. (Running on oeis4.)