A245995 T(n,k)=Number of length n+2 0..k arrays with no pair in any consecutive three terms totalling exactly k

2, 8, 2, 28, 12, 2, 64, 68, 18, 2, 126, 208, 164, 26, 2, 216, 534, 676, 396, 38, 2, 344, 1116, 2262, 2196, 956, 56, 2, 512, 2120, 5766, 9582, 7132, 2308, 82, 2, 730, 3648, 13064, 29790, 40590, 23168, 5572, 120, 2, 1000, 5930, 25992, 80504, 153906, 171942, 75260

Offset

1,1

Comments

Table starts

.2...8....28......64......126.......216........344.........512..........730

.2..12....68.....208......534......1116.......2120........3648.........5930

.2..18...164.....676.....2262......5766......13064.......25992........48170

.2..26...396....2196.....9582.....29790......80504......185192.......391290

.2..38...956....7132....40590....153906.....496088.....1319480......3178490

.2..56..2308...23168...171942....795144....3057032.....9401216.....25819210

.2..82..5572...75260...728358...4108062...18838280....66983128....209732170

.2.120.13452..244464..3085374..21223992..116086712...477250848...1703676570

.2.176.32476..794096.13069854.109652160..715358552..3400384160..13839144730

.2.258.78404.2579500.55364790.566509902.4408238024.24227537592.112416834410

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +a(n-3)

k=3: a(n) = 2*a(n-1) +a(n-2)

k=4: a(n) = 2*a(n-1) +a(n-2) +9*a(n-3) +3*a(n-4)

k=5: a(n) = 4*a(n-1) +a(n-2)

k=6: a(n) = 4*a(n-1) +a(n-2) +25*a(n-3) +5*a(n-4)

k=7: a(n) = 6*a(n-1) +a(n-2)

k=8: a(n) = 6*a(n-1) +a(n-2) +49*a(n-3) +7*a(n-4)

k=9: a(n) = 8*a(n-1) +a(n-2)

Empirical for row n:

n=1: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)

n=2: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7)

n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9)

n=4: [order 11]

n=5: [order 13]

n=6: [order 15]

n=7: [order 17]

Example

Some solutions for n=5 k=4
..3....0....4....0....0....4....2....1....0....1....1....3....4....1....3....2
..3....0....3....0....2....1....3....2....3....4....4....3....4....1....4....4
..3....3....2....0....0....2....3....0....0....4....4....4....3....0....2....4
..3....2....3....0....1....0....2....1....3....2....4....3....4....0....4....4
..2....4....0....2....0....3....0....0....2....1....3....4....2....1....3....4
..4....4....3....0....1....3....1....2....0....0....4....2....1....0....2....4
..1....1....0....0....2....2....1....3....0....2....3....4....1....1....0....3

Crossrefs

Sequence in context: A189217 A183037 A063077 * A085192 A320972 A273692

Adjacent sequences: A245992 A245993 A245994 * A245996 A245997 A245998

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 09 2014

Status

approved