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

1,1

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

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]

Example

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

Crossrefs

Sequence in context: A074916 A228375 A188966 * A091943 A318511 A345299

Adjacent sequences: A248430 A248431 A248432 * A248434 A248435 A248436

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 06 2014

Status

approved