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

1,1

Comments

Column 2 of A201072

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

Example

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

Crossrefs

Sequence in context: A178389 A297304 A155492 * A200931 A044159 A044540

Adjacent sequences: A201063 A201064 A201065 * A201067 A201068 A201069

Keyword

nonn

Author

R. H. Hardin Nov 26 2011

Status

approved