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A249290
T(n,k) = Number of length n+3 0..k arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.
14
14, 66, 26, 204, 168, 48, 524, 660, 428, 88, 1098, 2228, 2144, 1094, 162, 2070, 5646, 9504, 6960, 2792, 298, 3584, 12600, 29100, 40588, 22572, 7132, 548, 5808, 25280, 76856, 150112, 173368, 73204, 18232, 1008, 8934, 46608, 178644, 469072, 774542
OFFSET
1,1
COMMENTS
Table starts
...14.....66.....204.......524.......1098........2070.........3584.........5808
...26....168.....660......2228.......5646.......12600........25280........46608
...48....428....2144......9504......29100.......76856.......178644.......374540
...88...1094....6960.....40588.....150112......469072......1263044......3011088
..162...2792...22572....173368.....774542.....2863158......8930228.....24208540
..298...7132...73204....740616....3996816....17477172.....63142432....194636612
..548..18232..237480...3164312...20626236...106687006....446465388...1564897170
.1008..46616..770416..13520668..106449362...651265876...3156873140..12581992958
.1854.119176.2499164..57772560..549377682..3975630136..22321652802.101161030608
.3410.304696.8107012.246857788.2835311880.24269116850.157832259724.813349549954
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
k=2: [order 12]
k=3: [order 8]
k=4: [order 40]
k=5: [order 87]
Empirical for row n:
n=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-5) +2*a(n-6) -3*a(n-7) +a(n-8); also a polynomial of degree 4 plus a constant quasipolynomial with period 6
n=2: [order 32; also a polynomial of degree 5 plus a linear quasipolynomial with period 360]
EXAMPLE
Some solutions for n=4, k=4
..3....4....1....4....3....0....4....2....3....1....1....3....0....0....3....1
..2....0....4....1....2....1....4....3....0....1....0....2....3....2....2....0
..0....3....0....1....4....4....2....3....4....0....4....0....0....0....4....4
..2....3....4....4....4....1....3....2....4....0....3....2....4....0....0....4
..1....1....3....0....1....4....0....1....2....4....3....2....0....2....4....3
..0....4....2....4....4....4....1....4....0....1....3....0....1....1....0....0
..3....0....2....0....2....4....4....4....0....4....4....2....0....2....0....0
CROSSREFS
Column 1 is A135491(n+3).
Sequence in context: A226754 A058092 A213757 * A336744 A249291 A280401
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 24 2014
STATUS
approved