A247404 T(n,k)=Number of length n+4 0..k arrays with no disjoint pairs in any consecutive five terms having the same sum

0, 40, 0, 200, 40, 0, 760, 264, 40, 0, 2280, 1544, 340, 40, 0, 5640, 6216, 3200, 428, 40, 0, 12120, 19080, 17164, 6752, 528, 40, 0, 23800, 49032, 65500, 47592, 14456, 640, 40, 0, 43040, 113896, 201172, 225488, 132368, 31240, 864, 40, 0, 73840, 237456, 553328

Offset

1,2

Comments

Table starts

.0.40..200....760.....2280......5640......12120.......23800........43040

.0.40..264...1544.....6216.....19080......49032......113896.......237456

.0.40..340...3200....17164.....65500.....201172......553328......1328468

.0.40..428...6752....47592....225488.....826488.....2696652......7451396

.0.40..528..14456...132368....775668....3385192....13124760.....41711352

.0.40..640..31240...369064...2663568...13824356....63763868....232965764

.0.40..864..69976..1044356...9228900...56865236...311386556...1306471352

.0.40.1136.158392..2970580..32131008..234794368..1525127696...7342334396

.0.40.1456.359320..8447400.111936140..969917240..7475411480..41279228204

.0.40.1824.812952.23975404.389317160.4001182804.36618403600.231935339636

Links

R. H. Hardin, Table of n, a(n) for n = 1..1835

Formula

Empirical for column k:

k=1: a(n) = 0

k=2: a(n) = a(n-1)

k=3: a(n) = 6*a(n-5) -8*a(n-10)

k=4: [order 68]

Empirical for row n:

n=1: [linear recurrence of order 12; also polynomial of degree 5 plus quasipolynomial of degree 1 with period 12]

n=2: [linear recurrence of order 30]

Example

Some solutions for n=5 k=4
..2....2....0....1....0....2....2....0....2....3....1....4....0....0....3....4
..1....3....4....4....2....4....1....3....4....0....3....0....3....3....2....0
..4....0....4....0....4....0....0....2....1....0....3....3....0....2....0....3
..2....4....2....2....0....4....4....4....0....0....3....2....4....0....0....2
..2....0....1....0....3....3....0....4....0....1....0....0....0....4....4....0
..2....2....0....1....0....4....2....4....2....2....2....0....0....0....1....0
..3....0....0....0....2....4....0....1....0....4....3....4....2....0....2....4
..4....0....0....4....0....2....1....2....4....0....3....3....3....2....0....3
..2....3....4....0....4....4....4....0....1....0....3....2....4....3....4....0

Crossrefs

Sequence in context: A067159 A292152 A331907 * A013373 A013375 A013419

Adjacent sequences: A247401 A247402 A247403 * A247405 A247406 A247407

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 16 2014

Status

approved