A201095 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

28, 140, 140, 14, 728, 3696, 3273, 323, 10516, 37590, 22872, 1288, 52828, 199384, 125466, 8034, 251361, 795924, 417829, 19994, 734712, 2454383, 1348173, 72589, 2214440, 6602880, 3229480, 143081, 4945844, 15462250, 7894324, 387000, 11616040

Offset

1,1

Comments

Column 2 of A201101

Links

R. H. Hardin, Table of n, a(n) for n = 1..101

Formula

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

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

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

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

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

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

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

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

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

Example

Some solutions for n=10
..0..1....0..1....0..0....0..1....0..2....0..3....0..1....0..1....0..0....0..1
..0..2....0..1....0..2....0..2....0..3....0..3....0..2....0..2....0..2....0..2
..0..2....0..2....1..3....1..3....1..4....0..4....0..2....0..2....1..2....1..2
..1..5....2..4....1..3....2..4....1..4....1..4....1..4....1..3....1..3....1..3
..3..5....3..5....2..4....3..4....2..4....1..5....2..5....2..3....1..4....2..4
..3..6....3..5....2..4....3..5....2..5....2..5....3..6....4..5....3..5....3..4
..3..6....3..6....4..6....4..5....3..6....2..6....3..6....4..5....4..6....4..6
..4..7....4..6....5..6....5..6....3..7....3..6....4..7....4..6....5..7....5..6
..4..7....4..7....5..7....6..7....5..7....4..7....4..7....6..7....5..7....5..6
..4..7....6..7....7..7....6..7....6..7....6..7....5..7....7..7....6..7....7..7

Crossrefs

Sequence in context: A014705 A126415 A187047 * A239205 A050973 A095301

Adjacent sequences: A201092 A201093 A201094 * A201096 A201097 A201098

Keyword

nonn

Author

R. H. Hardin Nov 26 2011

Status

approved