A248537 T(n,k)=Number of length n+3 0..k arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth

2, 15, 2, 52, 15, 2, 101, 52, 15, 2, 198, 113, 52, 15, 2, 331, 246, 125, 52, 15, 2, 512, 427, 306, 137, 52, 15, 2, 753, 704, 555, 378, 149, 52, 15, 2, 1066, 1113, 992, 715, 462, 173, 52, 15, 2, 1439, 1654, 1673, 1412, 907, 594, 197, 52, 15, 2, 1908, 2279, 2606, 2535

Offset

1,1

Comments

Table starts

.2.15.52.101..198..331...512...753..1066...1439...1908...2461...3110...3867

.2.15.52.113..246..427...704..1113..1654...2279...3072...4045...5210...6555

.2.15.52.125..306..555...992..1673..2606...3663...5024...6777...8914..11379

.2.15.52.137..378..715..1412..2535..4142...5939...8300..11457..15402..19957

.2.15.52.149..462..907..2000..3827..6566...9607..13716..19361..26626..35005

.2.15.52.173..594.1219..2960..6069.10858..16099..23300..33707..47400..63085

.2.15.52.197..762.1635..4424..9681.18006..27031..39712..58889..84802.114305

.2.15.52.221..972.2167..6644.15501.29942..45525..67962.103197.152200.207761

.2.15.52.245.1230.2827..9968.24809.49734..76655.116444.180901.273222.377713

.2.15.52.293.1620.3895.15356.40799.84502.131445.201650.321447.496814.694263

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)

k=4: a(n) = a(n-1) +2*a(n-4) -2*a(n-5)

k=5: [order 17]

k=6: [order 17]

k=7: [order 25]

Empirical for row n:

n=1: a(n) = 2*a(n-1) -a(n-3) -a(n-4) +2*a(n-6) -a(n-7); also a cubic polynomial plus a constant quasipolynomial with period 6

n=2: [order 28; also a cubic polynomial plus a linear quasipolynomial with period 360]

Example

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

Crossrefs

Sequence in context: A201050 A299321 A357097 * A352000 A330073 A266584

Adjacent sequences: A248534 A248535 A248536 * A248538 A248539 A248540

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 08 2014

Status

approved