A201136 Number of n X 2 0..5 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

15, 30, 5, 135, 282, 51, 848, 1189, 120, 2596, 3978, 473, 7680, 9594, 836, 16302, 22017, 2208, 35248, 41604, 3380, 62174, 78404, 7167, 113125, 129100, 10067, 178415, 215500, 18583, 291000, 324765, 24652, 425790, 499302, 41363, 643958, 707364

Offset

1,1

Comments

Column 2 of A201142.

Links

R. H. Hardin, Table of n, a(n) for n = 1..183

Formula

Empirical: a(n) = a(n-3) +5*a(n-6) -5*a(n-9) -10*a(n-12) +10*a(n-15) +10*a(n-18) -10*a(n-21) -5*a(n-24) +5*a(n-27) +a(n-30) -a(n-33)

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

p=(n+5)/6: a(n) = 44*p^5 - (251/6)*p^4 + (29/2)*p^3 - (5/3)*p^2

q=(n+4)/6: a(n) = 44*q^5 - (53/4)*q^4 - 1*q^3 + (1/4)*q^2

r=(n+3)/6: a(n) = (44/15)*r^5 + (4/3)*r^4 + (1/2)*r^3 + (1/6)*r^2 + (1/15)*r

s=(n+2)/6: a(n) = 44*s^5 + (721/12)*s^4 + 26*s^3 + (53/12)*s^2 + (1/2)*s

t=(n+1)/6: a(n) = 44*t^5 + (629/6)*t^4 + (185/2)*t^3 + (107/3)*t^2 + 5*t

u=(n+0)/6: a(n) = (44/15)*u^5 + (133/12)*u^4 + 17*u^3 + (161/12)*u^2 + (167/30)*u + 1.

Example

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

Crossrefs

Sequence in context: A192356 A350468 A196184 * A200896 A322370 A040210

Adjacent sequences: A201133 A201134 A201135 * A201137 A201138 A201139

Keyword

nonn

Author

R. H. Hardin, Nov 27 2011

Status

approved