A249001 T(n,k)=Number of length n+4 0..k arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two

30, 190, 58, 820, 464, 112, 2540, 2668, 1140, 216, 6450, 10360, 8680, 2802, 416, 13990, 32398, 42308, 28240, 6872, 802, 27740, 82348, 163112, 172888, 91888, 16800, 1546, 50260, 189660, 485580, 822348, 706704, 299044, 41084, 2980, 86030, 387900

Offset

1,1

Comments

Table starts

....30....190......820......2540........6450........13990........27740

....58....464.....2668.....10360.......32398........82348.......189660

...112...1140.....8680.....42308......163112.......485580......1298968

...216...2802....28240....172888......822348......2865126......8902860

...416...6872....91888....706704.....4149708.....16909524.....61034658

...802..16800...299044...2888944....20952218.....99817384....418454994

..1546..41084...973204..11810564...105819690....589354152...2869206494

..2980.100590..3167500..48286456...534502810...3479916010..19673497892

..5744.246378.10309372.197422012..2700047696..20548067494.134897701458

.11072.603406.33554728.807188768.13640156760.121333048614.924972633722

Links

R. H. Hardin, Table of n, a(n) for n = 1..2018

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4)

k=2: [order 37]

k=3: [order 9]

Empirical for row n:

n=1: [linear recurrence of order 13; also a polynomial of degree 5 plus a quadratic quasipolynomial with period 6]

Example

Some solutions for n=4 k=4
..2....0....1....0....1....0....0....1....0....2....0....0....1....1....1....2
..1....0....1....2....0....2....3....0....4....3....2....4....1....3....0....1
..2....3....1....2....2....2....1....3....0....1....1....4....0....3....0....0
..2....0....3....2....0....2....3....2....1....4....3....2....2....1....1....4
..1....1....3....0....0....2....0....0....4....2....3....3....2....4....0....0
..3....4....0....2....0....4....0....2....0....2....4....4....3....0....1....0
..0....1....2....0....4....3....2....2....3....4....2....0....0....0....1....2
..1....2....0....4....0....3....4....0....1....4....1....2....0....3....0....0

Crossrefs

Column 1 is A135492(n+4)

Sequence in context: A071311 A337494 A265037 * A249466 A249002 A249467

Adjacent sequences: A248998 A248999 A249000 * A249002 A249003 A249004

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 18 2014

Status

approved