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A249290
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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
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14
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..9999
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FORMULA
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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]
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EXAMPLE
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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
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CROSSREFS
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Column 1 is A135491(n+3)
Sequence in context: A226754 A058092 A213757 * A336744 A249291 A280401
Adjacent sequences: A249287 A249288 A249289 * A249291 A249292 A249293
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Oct 24 2014
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STATUS
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approved
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