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 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 14

%I #6 Dec 12 2014 20:29:36

%S 30,190,58,820,464,112,2540,2668,1140,216,6450,10360,8680,2802,416,

%T 13990,32398,42308,28240,6872,802,27740,82348,163112,172888,91888,

%U 16800,1546,50260,189660,485580,822348,706704,299044,41084,2980,86030,387900

%N 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

%C Table starts

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

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

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

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

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

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

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

%C ..2980.100590..3167500..48286456...534502810...3479916010..19673497892

%C ..5744.246378.10309372.197422012..2700047696..20548067494.134897701458

%C .11072.603406.33554728.807188768.13640156760.121333048614.924972633722

%H R. H. Hardin, <a href="/A249001/b249001.txt">Table of n, a(n) for n = 1..2018</a>

%F Empirical for column k:

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

%F k=2: [order 37]

%F k=3: [order 9]

%F Empirical for row n:

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

%e Some solutions for n=4 k=4

%e ..2....0....1....0....1....0....0....1....0....2....0....0....1....1....1....2

%e ..1....0....1....2....0....2....3....0....4....3....2....4....1....3....0....1

%e ..2....3....1....2....2....2....1....3....0....1....1....4....0....3....0....0

%e ..2....0....3....2....0....2....3....2....1....4....3....2....2....1....1....4

%e ..1....1....3....0....0....2....0....0....4....2....3....3....2....4....0....0

%e ..3....4....0....2....0....4....0....2....0....2....4....4....3....0....1....0

%e ..0....1....2....0....4....3....2....2....3....4....2....0....0....0....1....2

%e ..1....2....0....4....0....3....4....0....1....4....1....2....0....3....0....0

%Y Column 1 is A135492(n+4)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 18 2014

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Last modified September 8 02:36 EDT 2024. Contains 375749 sequences. (Running on oeis4.)