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A248461
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T(n,k)=Number of length n+2 0..k arrays with no three consecutive terms having the sum of any two elements equal to twice the third
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13
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6, 18, 10, 48, 36, 16, 96, 148, 72, 26, 174, 380, 460, 144, 42, 282, 862, 1512, 1436, 288, 68, 432, 1652, 4272, 6040, 4488, 576, 110, 624, 2956, 9684, 21182, 24160, 14040, 1152, 178, 870, 4860, 20236, 56782, 105026, 96736, 43940, 2304, 288, 1170, 7642, 37868
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OFFSET
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1,1
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COMMENTS
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Table starts
...6...18......48.......96.......174........282.........432.........624
..10...36.....148......380.......862.......1652........2956........4860
..16...72.....460.....1512......4272.......9684.......20236.......37868
..26..144....1436.....6040.....21182......56782......138534......295078
..42..288....4488....24160....105026.....332940......948412.....2299356
..68..576...14040....96736....520788....1952254.....6493036....17917712
.110.1152...43940...387488...2582406...11447368....44452660...139623544
.178.2304..137532..1552448..12805334...67123652...304332258..1088015294
.288.4608..430508..6220480..63497776..393591402..2083523194..8478351478
.466.9216.1347652.24926080.314866606.2307892826.14264241960.66067495706
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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)
k=2: a(n) = 2*a(n-1)
k=3: a(n) = 2*a(n-1) +3*a(n-2) +4*a(n-3) -3*a(n-4) -12*a(n-5) -4*a(n-6)
k=4: a(n) = 3*a(n-1) +5*a(n-2) +2*a(n-3) -16*a(n-4) -28*a(n-5) -8*a(n-6)
k=5: [order 12]
k=6: [order 16]
k=7: [order 22]
Empirical for row n:
n=1: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5); also a cubic polynomial plus a constant quasipolynomial with period 2
n=2: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11); also a quartic polynomial plus a linear quasipolynomial with period 12
n=3: [order 27; also a degree 5 polynomial plus a quadratic quasipolynomial with period 840]
n=4: [order 61]
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EXAMPLE
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Some solutions for n=5 k=4
..3....4....4....0....1....4....3....1....0....0....1....1....1....1....3....4
..4....4....0....1....3....1....2....1....2....3....1....0....3....3....0....1
..4....1....4....1....0....2....3....4....3....1....0....1....4....4....3....1
..3....4....4....0....1....1....3....1....2....0....1....0....0....0....3....4
..0....0....1....4....1....2....2....4....3....1....4....3....0....0....4....1
..3....4....2....0....2....1....3....1....3....4....4....4....3....1....1....4
..3....3....4....0....2....1....2....2....4....2....0....4....1....3....1....4
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CROSSREFS
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Column 1 is A006355(n+4)
Column 2 is A005010
Sequence in context: A093061 A264028 A078741 * A129870 A331056 A274877
Adjacent sequences: A248458 A248459 A248460 * A248462 A248463 A248464
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Oct 06 2014
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STATUS
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approved
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