A248068 T(n,k)=Number of length n+5 0..k arrays with some disjoint triples in each consecutive six terms having the same sum

32, 333, 32, 1804, 513, 32, 6545, 3364, 793, 32, 18636, 15125, 6364, 1221, 32, 44677, 48316, 35529, 12124, 1861, 32, 94568, 131677, 128556, 83925, 23164, 2793, 32, 182049, 299968, 398737, 345760, 198333, 44284, 4113, 32, 325480, 625269, 983784

Offset

1,1

Comments

Table starts

.32...333...1804.....6545.....18636......44677......94568......182049

.32...513...3364....15125.....48316.....131677.....299968......625269

.32...793...6364....35529....128556.....398737.....983784.....2223873

.32..1221..12124....83925....345760....1220617....3273988.....8029409

.32..1861..23164...198333....933004....3747537...10950616....29138097

.32..2793..44284...467723...2517256...11500157...36646756...105799459

.32..4113..84604..1099415...6782344...35238445..122502768...383781973

.32..6753.161824..2676011..18295612..109996209..409950004..1407188901

.32.10945.309724..6485603..49388668..342828243.1372989004..5155470523

.32.17457.592924.15656957.133375284.1066829297.4600574912.18875673047

Links

R. H. Hardin, Table of n, a(n) for n = 1..565

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +20*a(n-6) -20*a(n-7) -64*a(n-12) +64*a(n-13)

k=3: [order 16]

Empirical for row n:

n=1: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7); also a degree 5 polynomial plus a quasipolynomial of degree zero with period 2

n=2: [order 16; also a degree 5 polynomial plus a cubic quasipolynomial with period 12]

Example

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

Crossrefs

Sequence in context: A201152 A223017 A293288 * A248069 A145402 A009797

Adjacent sequences: A248065 A248066 A248067 * A248069 A248070 A248071

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 30 2014

Status

approved