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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 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 2 of A201072
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin Nov 26 2011
STATUS
approved

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Last modified April 22 18:29 EDT 2024. Contains 371906 sequences. (Running on oeis4.)