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, 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

Author

R. H. Hardin, Oct 24 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A135491(n+3).

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]