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A250167
T(n,k)=Number of length n+1 0..k arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero
11
2, 3, 4, 4, 11, 8, 5, 20, 37, 16, 6, 33, 96, 119, 32, 7, 48, 211, 436, 373, 64, 8, 67, 380, 1269, 1880, 1151, 128, 9, 88, 639, 2860, 7109, 7836, 3517, 256, 10, 113, 976, 5831, 19896, 37881, 32032, 10679, 512, 11, 140, 1437, 10460, 49037, 129648, 195927
OFFSET
1,1
COMMENTS
Table starts
....2.....3.......4........5.........6..........7..........8...........9
....4....11......20.......33........48.........67.........88.........113
....8....37......96......211.......380........639........976........1437
...16...119.....436.....1269......2860.......5831......10460.......17765
...32...373....1880.....7109.....19896......49037.....103556......203615
...64..1151....7836....37881....129648.....380939.....938128.....2121089
..128..3517...32032...195927....810964....2810751....7989940....20567199
..256.10679..129572...996933...4962056...20169871...65768448...191480917
..512.32293..521256..5029417..30034672..142786013..532548628..1748028901
.1024.97391.2091052.25262121.180893724.1004527983.4281269376.15822382297
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 5*a(n-1) -6*a(n-2)
k=3: a(n) = 8*a(n-1) -21*a(n-2) +22*a(n-3) -8*a(n-4)
k=4: [order 8]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2
n=3: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a cubic polynomial plus a linear quasipolynomial with period 2
n=4: [order 12; also a quartic polynomial plus a quadratic quasipolynomial with period 12]
n=5: [order 24; also a polynomial of degree 5 plus a cubic quasipolynomialwith period 60]
EXAMPLE
Some solutions for n=5 k=4
..3....0....3....4....0....3....4....4....2....4....4....2....0....4....3....1
..2....0....4....2....0....4....1....4....4....1....3....1....1....2....1....1
..4....4....0....4....4....2....2....2....4....3....4....3....1....2....3....3
..0....2....0....1....2....1....3....2....1....0....3....2....3....1....0....4
..1....2....4....1....3....1....3....3....3....0....0....2....0....4....3....3
..1....0....3....2....0....1....2....4....0....4....0....2....0....2....3....1
CROSSREFS
Column 1 is A000079
Column 2 is A084171
Row 2 is A212959
Sequence in context: A240220 A250229 A250277 * A265534 A214554 A185417
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved