A200984 Number of nX2 0..4 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

10, 10, 20, 79, 21, 226, 157, 227, 678, 120, 1272, 789, 1015, 2697, 404, 4232, 2484, 3008, 7496, 1025, 10650, 6050, 7060, 16895, 2181, 22530, 12525, 14255, 33174, 4116, 42336, 23177, 25907, 59073, 7120, 72992, 39504, 43560, 97792, 11529, 117882, 63234

Offset: 1

Author

R. H. Hardin Nov 25 2011

Keywords

• nonn

Comments

Column 2 of A200990

Examples

			Some solutions for n=3
..0..1....0..2....0..1....0..3....0..2....0..1....0..1....0..2....0..2....0..2
..1..2....1..3....2..3....1..3....1..3....0..3....0..2....1..3....0..3....1..3
..3..4....4..4....2..4....2..4....2..4....2..4....3..4....3..4....1..4....1..4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 5*a(n-5) -10*a(n-10) +10*a(n-15) -5*a(n-20) +a(n-25)

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

p=(n+4)/5: a(n) = (115/6)*p^4 - 11*p^3 + (11/6)*p^2

q=(n+3)/5: a(n) = (115/12)*q^4 + (1/2)*q^3 - (1/12)*q^2

r=(n+2)/5: a(n) = (115/12)*r^4 + (49/6)*r^3 + (23/12)*r^2 + (1/3)*r

s=(n+1)/5: a(n) = (115/6)*s^4 + 35*s^3 + (125/6)*s^2 + 4*s

t=(n+0)/5: a(n) = (23/12)*t^4 + (37/6)*t^3 + (91/12)*t^2 + (13/3)*t + 1