A248433 T(n,k)=Number of length n+2 0..k arrays with every three consecutive terms having the sum of some two elements equal to twice the third.

2, 9, 2, 16, 9, 2, 29, 20, 9, 2, 42, 45, 24, 9, 2, 61, 70, 69, 28, 9, 2, 80, 105, 118, 101, 36, 9, 2, 105, 140, 185, 198, 165, 44, 9, 2, 130, 189, 252, 327, 342, 261, 52, 9, 2, 161, 242, 357, 462, 601, 590, 389, 68, 9, 2, 192, 301, 470, 691, 884, 1105, 1014, 645, 84, 9, 2, 229, 360

Offset: 1

Author

R. H. Hardin, Oct 06 2014

Keywords

• nonn
• tabl

Comments

Table starts

.2.9..16...29...42....61....80...105...130....161....192....229....266....309

.2.9..20...45...70...105...140...189...242....301....360....437....514....597

.2.9..24...69..118...185...252...357...470....593....716....881...1046...1217

.2.9..28..101..198...327...462...691...932...1203...1474...1829...2184...2551

.2.9..36..165..342...601...884..1381..1922...2533...3144...3957...4770...5613

.2.9..44..261..590..1105..1684..2775..3978...5365...6776...8639..10512..12467

.2.9..52..389.1014..2021..3200..5589..8218..11401..14696..18947..23274..27861

.2.9..68..645.1766..3761..6216.11317.17210..24491..32082..42077..52288..63213

.2.9..84.1029.3062..6969.11944.22921.35962..52505..70120..93459.117518.143619

.2.9.100.1541.5286.12815.22810.46415.74792.112443.153386.207401.264150.326755

Examples

			Some solutions for n=6 k=4
..2....3....3....0....4....3....1....4....0....2....3....0....2....0....2....1
..4....3....4....2....2....4....3....2....2....4....2....2....0....2....1....0
..0....3....2....4....0....2....2....3....1....3....1....4....4....1....0....2
..2....3....3....3....1....3....4....4....0....2....0....0....2....3....2....4
..1....3....4....2....2....4....3....2....2....1....2....2....0....2....4....0
..0....3....2....4....0....2....2....3....1....0....4....1....1....4....3....2
..2....3....0....3....1....0....4....4....0....2....0....3....2....3....2....4
..1....3....1....2....2....4....0....2....2....4....2....2....0....2....1....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)

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

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

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

k=6: a(n) = 8*a(n-3) -11*a(n-6) +4*a(n-9)

k=7: [order 13]

Empirical for row n:

n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also quadratic polynomial plus a constant quasipolynomial with period 2

n=2: a(n) = a(n-1) +a(n-3) -a(n-5) -a(n-7) +a(n-8); also a quadratic polynomial plus a constant quasipolynomial with period 12

n=3: [order 18; also a quadratic polynomial plus a constant quasipolynomial with period 840]

n=4: [order 36]

n=5: [order 70]