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.

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

Author

R. H. Hardin, Nov 13 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..263

Crossrefs

Column 1 is A000079

Column 2 is A084171

Row 2 is A212959

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]