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