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T(n,k)=Number of nonnegative integer arrays of length n+k+1 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value k+1
13

%I #4 Apr 21 2012 19:14:59

%S 1,1,7,1,11,33,1,16,77,146,1,22,157,461,664,1,29,289,1254,2621,3199,1,

%T 37,492,2997,9068,14862,16479,1,46,788,6451,27312,62617,86295,90774,1,

%U 56,1202,12766,72840,231046,426022,520534,532870,1,67,1762,23596,175475

%N T(n,k)=Number of nonnegative integer arrays of length n+k+1 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value k+1

%C Table starts

%C .....1......1.......1........1........1.........1.........1..........1

%C .....7.....11......16.......22.......29........37........46.........56

%C ....33.....77.....157......289......492.......788......1202.......1762

%C ...146....461....1254.....2997.....6451.....12766.....23596......41229

%C ...664...2621....9068....27312....72840....175475....388512.....801674

%C ..3199..14862...62617...231046...748964...2166176...5684153...13733643

%C .16479..86295..426022..1874580..7251376..24849643..76514893..214762865

%C .90774.520534.2913894.14904776.67580793.270933321.969656615.3138301423

%H R. H. Hardin, <a href="/A211836/b211836.txt">Table of n, a(n) for n = 1..9999</a>

%e Some solutions for n=3 k=4

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....1....1....1....1....0....1....1....1....1....1....1....1....1....1

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

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

%e ..4....4....4....4....3....3....2....4....3....2....4....3....1....0....4....3

%e ..5....2....5....0....4....4....3....1....4....3....5....4....4....4....5....4

%e ..3....5....4....5....0....5....4....4....5....4....2....0....2....5....0....3

%e ..5....3....3....0....5....4....5....5....3....5....2....5....5....3....2....5

%Y Row 2 is A000124(n+2)

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Apr 21 2012