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%I #5 Mar 31 2012 12:36:15
%S 2,4,2,5,6,2,7,7,8,2,8,12,11,10,2,10,12,20,16,12,2,11,18,21,32,22,14,
%T 2,13,17,36,33,49,28,16,2,14,24,31,64,54,70,34,18,2,16,22,49,51,110,
%U 84,94,40,20,2,17,30,42,95,91,179,119,120,46,22,2,19,27,63,76,179,157,275,157
%N T(n,k)=Number of nondecreasing arrangements of n+2 numbers in 0..k with the last equal to k and each after the second equal to the sum of one or two of the preceding four
%C Table starts
%C .2..4..5...7...8..10..11...13...14...16...17...19...20...22...23....25...26
%C .2..6..7..12..12..18..17...24...22...30...27...36...32...42...37....48...42
%C .2..8.11..20..21..36..31...49...42...63...51...79...60...93...72...105...80
%C .2.10.16..32..33..64..51...95...76..122...91..166..102..185..141...214..137
%C .2.12.22..49..54.110..91..179..154..238..190..360..215..376..333...453..290
%C .2.14.28..70..84.179.157..321..283..461..390..720..482..784..747...988..684
%C .2.16.34..94.119.275.253..548..477..845..725.1375..951.1608.1522..2126.1511
%C .2.18.40.120.157.393.374..866..775.1426.1261.2448.1761.3006.2890..4232.3063
%C .2.20.46.148.195.528.509.1267.1161.2230.2033.4069.3000.5252.5080..7749.5692
%C .2.22.52.178.233.676.649.1733.1606.3234.3005.6291.4691.8502.8350.13138.9724
%H R. H. Hardin, <a href="/A189326/b189326.txt">Table of n, a(n) for n = 1..3692</a>
%F Empirical: T(n,1) = 2
%F Empirical: T(n,2) = 2*n + 2
%F Empirical: T(n,3) = 6*n - 8 for n>3
%F Empirical: T(n,4) = n^2 + 11*n - 32 for n>5
%F Empirical: T(n,5) = 38*n - 147 for n>6
%F Empirical: T(n,6) = 6*n^2 + 34*n - 264 for n>8
%F Empirical: T(n,7) = 140*n - 751 for n>8
%F Empirical: T(n,8) = (1/3)*n^3 + 10*n^2 + (587/3)*n - 1558 for n>10
%e Some solutions for n=5 k=3
%e ..1....0....1....0....1....1....0....1....0....0....3....0....1....1....1....1
%e ..2....1....1....1....2....1....1....3....1....1....3....1....1....1....1....2
%e ..2....1....1....1....2....1....1....3....1....1....3....1....2....2....1....3
%e ..3....1....1....1....2....1....2....3....2....2....3....1....2....2....2....3
%e ..3....2....1....1....3....2....2....3....2....3....3....2....3....2....3....3
%e ..3....2....2....2....3....3....2....3....3....3....3....3....3....3....3....3
%e ..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
%Y Row 1 is A001651(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Apr 20 2011
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