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

Author

R. H. Hardin, Aug 09 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

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]