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%I #5 May 04 2013 18:24:20
%S 2,3,3,4,6,4,5,10,10,5,6,15,19,14,6,7,20,32,29,18,7,8,27,45,50,38,22,
%T 8,9,34,67,74,66,47,26,9,10,42,88,111,99,82,56,30,10,11,51,116,149,
%U 147,124,98,65,34,11,12,61,145,197,201,183,149,114,74,38,12,13,71,179,247,262
%N T(n,k)=Number of distinct values of the sum of i^2 over n realizations of i in 0..k
%C Table starts
%C ..2..3..4...5...6...7...8...9..10..11...12...13...14...15...16...17...18...19
%C ..3..6.10..15..20..27..34..42..51..61...71...83...94..106..120..135..148..165
%C ..4.10.19..32..45..67..88.116.145.179..212..260..300..347..402..464..517..592
%C ..5.14.29..50..74.111.149.197.247.308..370..451..526..613..706..815..914.1037
%C ..6.18.38..66..99.147.201.262.332.411..498..601..702..819..946.1078.1221.1375
%C ..7.22.47..82.124.183.250.326.414.513..621..749..874.1018.1176.1338.1515.1706
%C ..8.26.56..98.149.219.299.390.496.614..742..894.1045.1215.1404.1597.1807.2032
%C ..9.30.65.114.174.255.348.454.577.715..863.1038.1216.1412.1630.1856.2098.2357
%C .10.34.74.130.199.291.397.518.658.815..984.1182.1385.1608.1855.2114.2388.2681
%C .11.38.83.146.224.327.446.582.739.915.1105.1326.1554.1804.2080.2370.2677.3005
%H R. H. Hardin, <a href="/A225273/b225273.txt">Table of n, a(n) for n = 1..1325</a>
%F Empirical: column k is n*k^2 - A225277(k) for large n (n>36 suffices for k through 210)
%Y Row 1 is A000027(n+1)
%Y Row 2 is A047800
%Y Row 3 is A034966
%Y Row 4 is A047801
%Y Row 5 is A132432(n+1)
%Y Row 6 is A132438(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ May 04 2013