cp's OEIS Frontend

A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224145 #8 Aug 28 2018 05:56:03
%S A224145 29,239,1037,3296,8838,21183,46586,95455,184222,337727,592178,998751,
%T A224145 1627894,2574399,3963306,5956703,8761486,12638143,17910626,24977375,
%U A224145 34323558,46534591,62311002,82484703,108036734,140116543,180062866
%N A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224145 Column 7 of A224146.
%H A224145 R. H. Hardin, <a href="/A224145/b224145.txt">Table of n, a(n) for n = 1..210</a>
%F A224145 Empirical: a(n) = (4/315)*n^7 + (4/45)*n^6 + (34/45)*n^5 + (29/9)*n^4 + (508/45)*n^3 + (1156/45)*n^2 + (1328/35)*n - 161 for n>4.
%F A224145 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224145 G.f.: x*(29 + 7*x - 63*x^2 + 68*x^3 + 152*x^4 - 199*x^5 + 28*x^6 + 71*x^7 - 21*x^8 - 12*x^9 + 3*x^10 + x^11) / (1 - x)^8.
%F A224145 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.
%F A224145 (End)
%e A224145 Some solutions for n=3:
%e A224145 ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
%e A224145 ..0..0..1..1..1..1..0....0..0..1..0..0..0..0....0..0..0..1..1..1..0
%e A224145 ..0..0..1..1..1..1..1....0..0..1..0..0..0..0....0..0..0..1..1..1..1
%Y A224145 Cf. A224146.
%K A224145 nonn
%O A224145 1,1
%A A224145 _R. H. Hardin_, Mar 31 2013