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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 13
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 06 2014
STATUS
approved

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Last modified February 24 08:44 EST 2024. Contains 370294 sequences. (Running on oeis4.)