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.

21, 70, 35, 77, 749, 972, 127, 3034, 7161, 2170, 3258, 24178, 22584, 1925, 44526, 93370, 24434, 32166, 212694, 174093, 12492, 282808, 559380, 136472, 168016, 1042800, 794792, 51945, 1159645, 2215350, 518715, 613149, 3656445, 2665100

Offset: 1

Author

R. H. Hardin Nov 26 2011

Keywords

• nonn

Comments

Column 2 of A201072

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

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)

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

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

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

r=(n+4)/7: a(n) = (5887/180)*r^6 + (5/2)*r^5 - (7/36)*r^4 - (1/90)*r^2

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

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

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

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