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A202807 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

%I A202807 #13 Jun 02 2018 10:34:45
%S A202807 1,6,32,121,356,881,1925,3830,7083,12352,20526,32759,50518,75635,
%T A202807 110363,157436,220133,302346,408652,544389,715736,929797,1194689,
%U A202807 1519634,1915055,2392676,2965626,3648547,4457706,5411111,6528631,7832120,9345545
%N A202807 Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
%C A202807 Column 3 of A202812.
%H A202807 R. H. Hardin, <a href="/A202807/b202807.txt">Table of n, a(n) for n = 1..210</a>
%F A202807 Empirical: a(n) = (1/180)*n^6 + (1/20)*n^5 + (13/72)*n^4 - (67/360)*n^2 + (19/20)*n.
%F A202807 Conjectures from _Colin Barker_, Jun 02 2018: (Start)
%F A202807 G.f.: x*(1 - x + 11*x^2 - 12*x^3 + 6*x^4 - x^5) / (1 - x)^7.
%F A202807 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>7.
%F A202807 (End)
%e A202807 Some solutions for n=5:
%e A202807   0 0 0    0 0 0    0 0 0    0 0 0    0 0 0    0 0 0    0 0 0
%e A202807   0 0 0    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 0
%e A202807   0 1 2    0 0 1    0 0 1    0 0 0    0 1 2    0 1 1    0 0 2
%e A202807   0 2 2    0 2 3    0 1 3    0 0 2    0 2 2    0 2 2    0 1 2
%e A202807   0 2 4    0 2 3    0 2 4    0 1 3    0 2 2    0 2 2    0 2 2
%Y A202807 Cf. A202812.
%K A202807 nonn
%O A202807 1,2
%A A202807 _R. H. Hardin_, Dec 24 2011