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A201066 Number of nX2 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A201066 #7 Jul 22 2025 16:04:22
%S A201066 21,70,35,77,749,972,127,3034,7161,2170,3258,24178,22584,1925,44526,
%T A201066 93370,24434,32166,212694,174093,12492,282808,559380,136472,168016,
%U A201066 1042800,794792,51945,1159645,2215350,518715,613149,3656445,2665100
%N A201066 Number of nX2 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A201066 Column 2 of A201072
%H A201066 R. H. Hardin, <a href="/A201066/b201066.txt">Table of n, a(n) for n = 1..126</a>
%F A201066 Empirical: a(n) = 7*a(n-7) -21*a(n-14) +35*a(n-21) -35*a(n-28) +21*a(n-35) -7*a(n-42) +a(n-49)
%F A201066 Subsequences for n modulo 7 = 1,2,3,4,5,6,0
%F A201066 p=(n+6)/7: a(n) = (5887/60)*p^6 - (799/6)*p^5 + (287/4)*p^4 - (52/3)*p^3 + (49/30)*p^2
%F A201066 q=(n+5)/7: a(n) = (5887/36)*q^6 - (673/6)*q^5 + (151/9)*q^4 + (13/6)*q^3 - (11/36)*q^2
%F A201066 r=(n+4)/7: a(n) = (5887/180)*r^6 + (5/2)*r^5 - (7/36)*r^4 - (1/90)*r^2
%F A201066 s=(n+3)/7: a(n) = (5887/180)*s^6 + (458/15)*s^5 + (365/36)*s^4 + (17/6)*s^3 + (59/90)*s^2 + (2/15)*s
%F A201066 t=(n+2)/7: a(n) = (5887/36)*t^6 + (925/3)*t^5 + (7489/36)*t^4 + (121/2)*t^3 + (143/18)*t^2 + (2/3)*t
%F A201066 u=(n+1)/7: a(n) = (5887/60)*u^6 + (862/3)*u^5 + (4007/12)*u^4 + (1153/6)*u^3 + (817/15)*u^2 + 6*u
%F A201066 v=(n+0)/7: a(n) = (841/180)*v^6 + (101/5)*v^5 + (1325/36)*v^4 + (73/2)*v^3 + (946/45)*v^2 + (34/5)*v + 1
%e A201066 Some solutions for n=10
%e A201066 ..0..3....0..1....0..2....0..0....0..0....0..0....0..1....0..0....0..1....0..1
%e A201066 ..0..3....0..3....0..2....0..1....0..1....1..2....0..1....0..2....0..1....0..1
%e A201066 ..0..4....1..3....1..3....1..2....1..3....1..2....0..3....1..2....0..2....0..2
%e A201066 ..1..4....1..3....1..3....1..2....2..3....1..3....1..4....1..2....1..2....1..2
%e A201066 ..1..4....2..4....1..3....3..3....2..3....2..4....2..4....3..5....2..3....2..4
%e A201066 ..1..5....2..4....2..4....3..5....2..4....3..4....2..4....3..5....3..3....3..4
%e A201066 ..2..5....2..4....4..5....4..5....4..5....3..5....3..5....3..5....4..4....3..5
%e A201066 ..2..5....5..6....4..5....4..5....4..5....4..6....3..5....4..6....5..6....3..5
%e A201066 ..2..6....5..6....5..6....4..6....5..6....5..6....5..6....4..6....5..6....5..6
%e A201066 ..6..6....5..6....6..6....6..6....6..6....5..6....6..6....4..6....5..6....6..6
%K A201066 nonn
%O A201066 1,1
%A A201066 _R. H. Hardin_ Nov 26 2011