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%I #7 Oct 15 2023 13:14:22
%S 1,2,1,3,3,1,4,6,4,1,5,9,9,5,1,6,14,15,12,6,1,7,19,26,21,15,7,1,8,25,
%T 36,36,27,18,8,1,9,32,49,51,46,33,21,9,1,10,39,66,71,66,56,39,24,10,1,
%U 11,47,85,94,92,81,66,45,27,11,1,12,56,103,123,122,113,96,76,51,30,12,1,13,64
%N T(n,k) = Number of distinct values of the sum of i*(i-1) over n realizations of i in 0..k.
%C Table starts
%C .1..2..3..4..5...6...7...8...9..10..11..12..13..14..15...16...17...18...19...20
%C .1..3..6..9.14..19..25..32..39..47..56..64..76..87..99..109..123..138..152..167
%C .1..4..9.15.26..36..49..66..85.103.130.152.180.214.247..276..320..362..399..444
%C .1..5.12.21.36..51..71..94.123.150.188.223.263.310.359..409..465..523..586..653
%C .1..6.15.27.46..66..92.122.160.195.243.290.344.403.466..532..605..680..762..848
%C .1..7.18.33.56..81.113.150.196.240.298.356.423.495.571..653..744..835..936.1040
%C .1..8.21.39.66..96.134.178.232.285.353.422.501.586.676..773..881..989.1107.1232
%C .1..9.24.45.76.111.155.206.268.330.408.488.579.677.781..893.1017.1143.1278.1423
%C .1.10.27.51.86.126.176.234.304.375.463.554.657.768.886.1013.1153.1296.1449.1614
%C .1.11.30.57.96.141.197.262.340.420.518.620.735.859.991.1133.1289.1449.1620.1804
%H R. H. Hardin, <a href="/A225281/b225281.txt">Table of n, a(n) for n = 1..1325</a>
%F Empirical: column k is n*k*(k-1)/2 - A225288(k) for large n (n>37 is sufficient through k=389).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 04 2013
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