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A250419
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
12
3, 5, 6, 7, 17, 10, 9, 36, 38, 20, 11, 65, 99, 125, 36, 13, 106, 205, 476, 335, 72, 15, 161, 370, 1351, 1693, 1061, 136, 17, 232, 606, 3154, 5982, 7504, 3069, 272, 19, 321, 927, 6433, 16790, 34415, 29221, 9495, 528, 21, 430, 1345, 11906, 39916, 119364, 169352
OFFSET
1,1
COMMENTS
Table starts
....3.....5.......7........9........11........13.........15..........17
....6....17......36.......65.......106.......161........232.........321
...10....38......99......205.......370.......606........927........1345
...20...125.....476.....1351......3154......6433......11906.......20461
...36...335....1693.....5982.....16790.....39916......84094......161350
...72..1061....7504....34415....119364....341011.....845358.....1878315
..136..3069...29221...169352....713260...2399000....6847916....17247435
..272..9495..123242...904695...4620694..18334295...60473968...173147889
..528.28221..492076..4547008..28033122.130350889..493271080..1595410130
.1056.86149.2021436.23448029.174036890.947356115.4110606460.15000578409
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3)
k=2: [order 10]
k=3: [order 29]
Empirical for row n:
n=1: a(n) = 2*n + 1
n=2: a(n) = (1/3)*n^3 + 2*n^2 + (8/3)*n + 1
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
n=4: [linear recurrence of order 10; also a quintic polynomial plus a linear quasipolynomial with period 3]
n=5: [order 17; also a quintic polynomial plus a quadratic quasipolynomial with period 12]
EXAMPLE
Some solutions for n=5 k=4
..3....0....3....1....3....3....2....1....2....0....0....1....2....4....0....3
..1....2....1....0....4....2....0....3....1....0....0....0....4....0....2....0
..4....0....0....0....1....4....3....2....2....0....1....0....3....2....2....0
..3....2....2....2....4....2....0....0....1....2....1....4....2....1....4....2
..2....3....3....0....4....4....4....3....2....1....4....1....3....4....1....1
..1....2....1....1....3....4....0....3....3....1....0....3....3....0....2....1
CROSSREFS
Column 1 is A005418(n+2)
Row 1 is A004273(n+1)
Row 2 is A084990(n+1)
Sequence in context: A274928 A163620 A227722 * A072134 A179220 A290577
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 22 2014
STATUS
approved