A201095 - OEIS

%I #5 Mar 31 2012 12:36:43

%S 28,140,140,14,728,3696,3273,323,10516,37590,22872,1288,52828,199384,

%T 125466,8034,251361,795924,417829,19994,734712,2454383,1348173,72589,

%U 2214440,6602880,3229480,143081,4945844,15462250,7894324,387000,11616040

%N Number of nX2 0..7 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

%C Column 2 of A201101

%H R. H. Hardin, <a href="/A201095/b201095.txt">Table of n, a(n) for n = 1..101</a>

%F Subsequences for n modulo 8 = 1,2,3,4,5,6,7,0

%F p=(n+7)/8: a(n) = (9664/45)*p^7 - (3831/10)*p^6 + (10235/36)*p^5 - (641/6)*p^4 + (3679/180)*p^3 - (47/30)*p^2

%F q=(n+6)/8: a(n) = (4832/9)*q^7 - (3523/6)*q^6 + (7607/36)*q^5 - (109/6)*q^4 - (115/36)*q^3 + (1/3)*q^2

%F r=(n+5)/8: a(n) = (9664/45)*r^7 - (6197/90)*r^6 - (259/36)*r^5 + (23/18)*r^4 - (11/180)*r^3 + (7/90)*r^2

%F s=(n+4)/8: a(n) = (2416/315)*s^7 + (172/45)*s^6 + (14/9)*s^5 + (43/72)*s^4 + (43/180)*s^3 + (29/360)*s^2 + (1/28)*s

%F t=(n+3)/8: a(n) = (9664/45)*t^7 + (9209/30)*t^6 + (27949/180)*t^5 + (81/2)*t^4 + (1579/180)*t^3 + (23/15)*t^2 + (1/5)*t

%F u=(n+2)/8: a(n) = (4832/9)*u^7 + (23255/18)*u^6 + (43211/36)*u^5 + (19297/36)*u^4 + (4229/36)*u^3 + (451/36)*u^2 + (5/6)*u

%F v=(n+1)/8: a(n) = (9664/45)*v^7 + (22331/30)*v^6 + (38495/36)*v^5 + (2443/3)*v^4 + (62269/180)*v^3 + (773/10)*v^2 + 7*v

%F w=(n+0)/8: a(n) = (2416/315)*w^7 + (3353/90)*w^6 + (14089/180)*w^5 + (6679/72)*w^4 + (3037/45)*w^3 + (10973/360)*w^2 + (3389/420)*w + 1

%e Some solutions for n=10

%e ..0..1....0..1....0..0....0..1....0..2....0..3....0..1....0..1....0..0....0..1

%e ..0..2....0..1....0..2....0..2....0..3....0..3....0..2....0..2....0..2....0..2

%e ..0..2....0..2....1..3....1..3....1..4....0..4....0..2....0..2....1..2....1..2

%e ..1..5....2..4....1..3....2..4....1..4....1..4....1..4....1..3....1..3....1..3

%e ..3..5....3..5....2..4....3..4....2..4....1..5....2..5....2..3....1..4....2..4

%e ..3..6....3..5....2..4....3..5....2..5....2..5....3..6....4..5....3..5....3..4

%e ..3..6....3..6....4..6....4..5....3..6....2..6....3..6....4..5....4..6....4..6

%e ..4..7....4..6....5..6....5..6....3..7....3..6....4..7....4..6....5..7....5..6

%e ..4..7....4..7....5..7....6..7....5..7....4..7....4..7....6..7....5..7....5..6

%e ..4..7....6..7....7..7....6..7....6..7....6..7....5..7....7..7....6..7....7..7

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 26 2011