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

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

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

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

Adjacent sequences: A248458 A248459 A248460 * A248462 A248463 A248464

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 06 2014

Status

approved