|
%I #8 Apr 05 2018 11:13:21
%S 1,1,136,664,1720,3491,6263,10400,16357,24694,36091,51364,71482,97585,
%T 131003,173276,226175,291724,372223,470272,588796,731071,900751,
%U 1101896,1339001,1617026,1941427,2318188,2753854,3255565,3831091,4488868,5238035
%N Number of nondecreasing arrangements of n+3 numbers in 0..6 with each number being the sum mod 7 of three others.
%C Column 6 of A183904.
%H R. H. Hardin, <a href="/A183901/b183901.txt">Table of n, a(n) for n = 1..37</a>
%F Empirical: a(n) = (1/720)*n^6 + (13/240)*n^5 + (125/144)*n^4 + (117/16)*n^3 + (12287/360)*n^2 - (4421/30)*n - 44 for n>3.
%F Conjectures from _Colin Barker_, Apr 05 2018: (Start)
%F G.f.: x*(1 - 6*x + 150*x^2 - 302*x^3 - 72*x^4 + 649*x^5 - 548*x^6 + 60*x^7 + 102*x^8 - 33*x^9) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.
%F (End)
%e Some solutions for n=3:
%e ..0....0....3....0....0....0....0....0....0....0....0....1....0....0....2....1
%e ..1....0....3....1....0....0....0....3....2....1....1....1....3....0....4....2
%e ..1....1....3....1....1....3....1....4....3....2....4....2....3....1....4....3
%e ..2....1....4....4....2....3....1....5....4....3....5....3....4....2....5....3
%e ..4....2....4....4....2....5....3....6....4....4....5....4....5....4....5....5
%e ..4....4....4....6....4....6....3....6....6....4....6....5....5....4....6....6
%Y Cf. A183904.
%K nonn
%O 1,3
%A _R. H. Hardin_, Jan 07 2011
| 