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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A014095 A192356 A196184 * A200896 A322370 A040210

Adjacent sequences:  A201133 A201134 A201135 * A201137 A201138 A201139

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 27 2011

STATUS

approved

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Last modified December 7 20:04 EST 2021. Contains 349585 sequences. (Running on oeis4.)