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A248461
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
13
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Column 1 is A006355(n+4)
Column 2 is A005010
Sequence in context: A093061 A264028 A078741 * A129870 A331056 A274877
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 06 2014
STATUS
approved