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%I #8 Apr 06 2018 07:00:59
%S 1,1,22,136,470,1193,2525,4752,8238,13438,20912,31340,45538,64475,
%T 89291,121316,162090,213384,277222,355904,452030,568525,708665,876104,
%U 1074902,1309554,1585020,1906756,2280746,2713535,3212263,3784700,4439282,5185148
%N Number of nondecreasing arrangements of n+2 numbers in 0..6 with each number being the sum mod 7 of two others.
%C Column 6 of A183912.
%H R. H. Hardin, <a href="/A183909/b183909.txt">Table of n, a(n) for n = 1..76</a>
%F Empirical: a(n) = (1/720)*n^6 + (11/240)*n^5 + (89/144)*n^4 + (209/48)*n^3 - (13003/360)*n^2 + (531/10)*n + 12 for n>3.
%F Conjectures from _Colin Barker_, Apr 06 2018: (Start)
%F G.f.: x*(1 - 6*x + 36*x^2 - 32*x^3 - 20*x^4 + 3*x^5 + 40*x^6 - 16*x^7 - 9*x^8 + 4*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 All solutions for n=2:
%e ..0
%e ..0
%e ..0
%e ..0
%Y Cf. A183912.
%K nonn
%O 1,3
%A _R. H. Hardin_, Jan 07 2011
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