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

1,1

Comments

Column 2 of A200990

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

Example

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

Crossrefs

Sequence in context: A076817 A324494 A344104 * A361037 A299576 A185993

Adjacent sequences: A200981 A200982 A200983 * A200985 A200986 A200987

Keyword

nonn

Author

R. H. Hardin Nov 25 2011

Status

approved