A247995 T(n,k)=Number of length n+5 0..k arrays with no disjoint triples in any consecutive six terms having the same sum

32, 396, 32, 2292, 702, 32, 9080, 5316, 1264, 32, 28020, 27800, 12612, 2314, 32, 72972, 104620, 86736, 30404, 4308, 32, 167576, 329742, 397988, 274204, 74132, 8150, 32, 349392, 884032, 1514488, 1530604, 874884, 182084, 15640, 32, 674520, 2131356

Offset

1,1

Comments

Table starts

.32....396....2292......9080......28020.......72972.......167576........349392

.32....702....5316.....27800.....104620......329742.......884032.......2131356

.32...1264...12612.....86736.....397988.....1514488......4733944......13169096

.32...2314...30404....274204....1530604.....7023686.....25559480......81945184

.32...4308...74132....874884....5921416....32751572....138568024.....511733540

.32...8150..182084...2808970...22963328...153115250....752268668....3199929582

.32..15640..448956...9057366...89060732...716467630...4083208500...20012299980

.32..30620.1112546..29402376..346013066..3360812402..22177936206..125265598534

.32..60192.2766188..95651698.1346084716.15777745722.120522456308..784380367170

.32.118756.6890602.311754322.5240401580.74117488694.655151391416.4912998973440

Links

R. H. Hardin, Table of n, a(n) for n = 1..468

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 2*a(n-1) +10*a(n-6) -20*a(n-7) -16*a(n-12) +32*a(n-13)

Empirical for row n:

n=1: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8); also polynomial of degree 6 plus a degree 0 quasipolynomial with period 2

n=2: [order 18; also polynomial of degree 7 plus a cubic quasipolynomial with period 12]

Example

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

Crossrefs

Sequence in context: A087024 A128798 A086942 * A247996 A068548 A195191

Adjacent sequences: A247992 A247993 A247994 * A247996 A247997 A247998

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 28 2014

Status

approved