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%I A225007 #41 Feb 22 2024 20:31:34
%S A225007 1,16,86,296,791,1792,3612,6672,11517,18832,29458,44408,64883,92288,
%T A225007 128248,174624,233529,307344,398734,510664,646415,809600,1004180,
%U A225007 1234480,1505205,1821456,2188746,2613016,3100651,3658496,4293872,5014592,5828977
%N A225007 Number of n X 5 0..1 arrays with rows unimodal and columns nondecreasing.
%H A225007 Andrew Howroyd, <a href="/A225007/b225007.txt">Table of n, a(n) for n = 0..1000</a> (terms 1..210 from R. H. Hardin)
%F A225007 a(n) = (2/15)*n^5 + (7/6)*n^4 + (23/6)*n^3 + (35/6)*n^2 + (121/30)*n + 1.
%F A225007 6*a(n) = Sum_{i=1..n+1} A000384(i)*A000384(i+1). - _Bruno Berselli_, Feb 05 2014
%F A225007 From _Colin Barker_, Mar 16 2018: (Start)
%F A225007 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n >= 6.
%F A225007 G.f.: (1 + 10*x + 5*x^2) / (1 - x)^6. (End)
%e A225007 Some solutions for n=3:
%e A225007   0 0 0 0 0    0 0 1 0 0    0 0 1 1 1    0 0 1 1 0
%e A225007   0 0 0 1 0    0 1 1 0 0    0 0 1 1 1    0 0 1 1 1
%e A225007   0 0 1 1 0    0 1 1 1 0    0 0 1 1 1    0 1 1 1 1
%e A225007 6*a(7) = 40032 = 1*6 + 6*15 + 15*28 + 28*45 + 45*66 + 66*91 + 91*120 + 120*153. - _Bruno Berselli_, Feb 05 2014
%Y A225007 Column 5 of A225010.
%K A225007 nonn,easy
%O A225007 0,2
%A A225007 _R. H. Hardin_, Apr 23 2013
%E A225007 a(0)=1 prepended by _Andrew Howroyd_, Feb 11 2024

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