A247404 - OEIS

%I #6 Dec 12 2014 20:42:02

%S 0,40,0,200,40,0,760,264,40,0,2280,1544,340,40,0,5640,6216,3200,428,

%T 40,0,12120,19080,17164,6752,528,40,0,23800,49032,65500,47592,14456,

%U 640,40,0,43040,113896,201172,225488,132368,31240,864,40,0,73840,237456,553328

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

%C Table starts

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

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

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

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

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

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

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

%C .0.40.1136.158392..2970580..32131008..234794368..1525127696...7342334396

%C .0.40.1456.359320..8447400.111936140..969917240..7475411480..41279228204

%C .0.40.1824.812952.23975404.389317160.4001182804.36618403600.231935339636

%H R. H. Hardin, <a href="/A247404/b247404.txt">Table of n, a(n) for n = 1..1835</a>

%F Empirical for column k:

%F k=1: a(n) = 0

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

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

%F k=4: [order 68]

%F Empirical for row n:

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

%F n=2: [linear recurrence of order 30]

%e Some solutions for n=5 k=4

%e ..2....2....0....1....0....2....2....0....2....3....1....4....0....0....3....4

%e ..1....3....4....4....2....4....1....3....4....0....3....0....3....3....2....0

%e ..4....0....4....0....4....0....0....2....1....0....3....3....0....2....0....3

%e ..2....4....2....2....0....4....4....4....0....0....3....2....4....0....0....2

%e ..2....0....1....0....3....3....0....4....0....1....0....0....0....4....4....0

%e ..2....2....0....1....0....4....2....4....2....2....2....0....0....0....1....0

%e ..3....0....0....0....2....4....0....1....0....4....3....4....2....0....2....4

%e ..4....0....0....4....0....2....1....2....4....0....3....3....3....2....0....3

%e ..2....3....4....0....4....4....4....0....1....0....3....2....4....3....4....0

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Sep 16 2014