A250419 - OEIS

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

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

(list; table; graph; refs; listen; history; text; internal format)

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

R. H. Hardin, Table of n, a(n) for n = 1..313

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

Adjacent sequences: A250416 A250417 A250418 * A250420 A250421 A250422

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 22 2014

STATUS

approved