A250419 - OEIS

%I #6 Dec 12 2014 20:49:20

%S 3,5,6,7,17,10,9,36,38,20,11,65,99,125,36,13,106,205,476,335,72,15,

%T 161,370,1351,1693,1061,136,17,232,606,3154,5982,7504,3069,272,19,321,

%U 927,6433,16790,34415,29221,9495,528,21,430,1345,11906,39916,119364,169352

%N T(n,k)=Number of length n+1 0..k arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero

%C Table starts

%C ....3.....5.......7........9........11........13.........15..........17

%C ....6....17......36.......65.......106.......161........232.........321

%C ...10....38......99......205.......370.......606........927........1345

%C ...20...125.....476.....1351......3154......6433......11906.......20461

%C ...36...335....1693.....5982.....16790.....39916......84094......161350

%C ...72..1061....7504....34415....119364....341011.....845358.....1878315

%C ..136..3069...29221...169352....713260...2399000....6847916....17247435

%C ..272..9495..123242...904695...4620694..18334295...60473968...173147889

%C ..528.28221..492076..4547008..28033122.130350889..493271080..1595410130

%C .1056.86149.2021436.23448029.174036890.947356115.4110606460.15000578409

%H R. H. Hardin, <a href="/A250419/b250419.txt">Table of n, a(n) for n = 1..313</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)

%F k=2: [order 10]

%F k=3: [order 29]

%F Empirical for row n:

%F n=1: a(n) = 2*n + 1

%F n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1

%F n=3: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5); also a cubic polynomial plus a constant quasipolynomial with period 2

%F n=4: [linear recurrence of order 10; also a quintic polynomial plus a linear quasipolynomial with period 3]

%F n=5: [order 17; also a quintic polynomial plus a quadratic quasipolynomial with period 12]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 1 is A005418(n+2)

%Y Row 1 is A004273(n+1)

%Y Row 2 is A084990(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 22 2014