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A202752 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.

%I A202752 #8 Jun 01 2018 11:57:38
%S A202752 1,4,17,62,184,462,1022,2052,3819,6688,11143,17810,27482,41146,60012,
%T A202752 85544,119493,163932,221293,294406,386540,501446,643402,817260,
%U A202752 1028495,1283256,1588419,1951642,2381422,2887154,3479192,4168912,4968777,5892404
%N A202752 Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
%C A202752 Column 4 of A202756.
%H A202752 R. H. Hardin, <a href="/A202752/b202752.txt">Table of n, a(n) for n = 1..210</a>
%F A202752 Empirical: a(n) = (1/360)*n^6 + (1/30)*n^5 + (5/72)*n^4 - (1/6)*n^3 + (77/180)*n^2 + (19/30)*n.
%F A202752 Conjectures from _Colin Barker_, Jun 01 2018: (Start)
%F A202752 G.f.: x*(1 - 3*x + 10*x^2 - 8*x^3 + 2*x^4) / (1 - x)^7.
%F A202752 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 A202752 (End)
%e A202752 Some solutions for n=5:
%e A202752 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A202752 ..0..0..0..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
%e A202752 ..0..0..0..1....0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..1
%e A202752 ..0..1..1..1....0..0..1..2....0..0..0..1....0..1..2..2....0..0..1..2
%e A202752 ..0..1..1..2....0..1..2..3....0..1..1..2....0..1..2..2....0..1..2..2
%Y A202752 Cf. A202756.
%K A202752 nonn
%O A202752 1,2
%A A202752 _R. H. Hardin_, Dec 23 2011