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A190041 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 three 14

%I

%S 2,4,2,5,6,2,7,7,8,2,8,12,10,10,2,10,12,18,14,12,2,11,18,16,27,18,14,

%T 2,13,17,30,23,39,22,16,2,14,24,22,47,33,53,26,18,2,16,22,40,31,72,45,

%U 69,30,20,2,17,30,31,65,43,107,57,87,34,22,2,19,27,49,49,105,60,151,69,107

%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 three

%C Table starts

%C .2..4..5...7..8..10..11..13..14..16..17...19..20...22...23...25..26...28..29

%C .2..6..7..12.12..18..17..24..22..30..27...36..32...42...37...48..42...54..47

%C .2..8.10..18.16..30..22..40..31..49..36...64..41...71...53...81..55...97..61

%C .2.10.14..27.23..47..31..65..49..76..52..113..58..109...92..132..78..167..87

%C .2.12.18..39.33..72..43.105..69.123..72..190..83..169..151..217.108..276.120

%C .2.14.22..53.45.107..60.164.100.189..99..311.121..251..241..358.146..447.167

%C .2.16.26..69.57.151..80.246.144.284.138..492.178..372..364..583.195..717.239

%C .2.18.30..87.69.203.100.349.200.409.189..754.258..545..540..927.267.1109.341

%C .2.20.34.107.81.263.120.472.264.560.245.1108.352..775..778.1424.364.1677.484

%C .2.22.38.129.93.331.140.617.336.735.301.1561.448.1053.1072.2094.474.2449.657

%H R. H. Hardin, <a href="/A190041/b190041.txt">Table of n, a(n) for n = 1..4434</a>

%F Empirical: T(n,1) = 2

%F Empirical: T(n,2) = 2*n + 2

%F Empirical: T(n,3) = 4*n - 2 for n>2

%F Empirical: T(n,4) = n^2 + 3*n - 1 for n>3

%F Empirical: T(n,5) = 12*n - 27 for n>4

%F Empirical: T(n,6) = 4*n^2 - 8*n + 11 for n>5

%F Empirical: T(n,7) = 20*n - 60 for n>5

%F Empirical: T(n,8) = (1/3)*n^3 + 2*n^2 + (50/3)*n - 83 for n>6

%e Some solutions for n=5 k=3

%e ..2....3....1....1....0....1....0....0....0....0....1....1....1....1....1....1

%e ..3....3....1....1....1....2....1....1....1....3....1....3....1....1....1....2

%e ..3....3....2....1....1....3....1....1....1....3....1....3....1....1....2....2

%e ..3....3....3....1....1....3....2....1....2....3....1....3....1....2....2....3

%e ..3....3....3....2....1....3....3....2....2....3....1....3....2....3....3....3

%e ..3....3....3....3....2....3....3....3....3....3....2....3....2....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)

%Y Row 2 is A189327

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 04 2011

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Last modified September 22 17:01 EDT 2021. Contains 347607 sequences. (Running on oeis4.)