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

1,1

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

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

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

Adjacent sequences: A250164 A250165 A250166 * A250168 A250169 A250170

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2014

Status

approved