A185567 -id:A185567 - cp's OEIS frontend

A185565 1/4 the number of nX7 0..3 arrays with no element equal both to the element above and to the element to its left.

4096, 45562500, 504547256880, 5586628402633500, 61858104930689319360, 684925618712729136913980, 7583858300260627032845531520, 83972485690826213759616527499540, 929787724653148422947168982361958940

Offset: 1

R. H. Hardin Jan 31 2011

nonn

Column 7 of A185567

			Some solutions for 3X7 with a(1,1)=0
..0..0..0..0..0..0..1....0..0..0..0..1..1..2....0..0..0..0..2..0..2
..0..2..0..2..2..1..3....0..2..0..2..0..0..2....0..2..0..2..1..0..2
..0..0..2..0..0..1..3....0..0..2..0..1..0..3....0..0..2..0..1..3..0

R. H. Hardin, Table of n, a(n) for n = 1..200

A185560 1/4 the number of n X n 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

1, 60, 50580, 598507920, 99407416968000, 231753101877188629380, 7583858300260627032845531520, 3483475434832751291309593655505225600, 22459143127863154464679826472043109609252549520

Offset: 1

R. H. Hardin Jan 31 2011

nonn

Diagonal of A185567

			Some solutions for 3X3 with a(1,1)=0
..0..1..2....0..3..2....0..0..0....0..3..2....0..2..1....0..0..0....0..0..3
..3..1..1....1..2..0....1..2..2....0..0..0....1..3..0....0..2..0....3..3..0
..3..3..1....1..2..0....3..3..3....1..1..3....0..1..3....0..0..2....0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..10

A185561 1/4 the number of n X 3 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

16, 900, 50580, 2842560, 159749820, 8977824540, 504547256880, 28355191537860, 1593541291098420, 89555869973406240, 5032975230384726780, 282849573983126145660, 15895941831670877597520, 893340453575999346503940

Offset: 1

R. H. Hardin, Jan 31 2011

nonn

Column 3 of A185567.

			Some solutions for 5 X 3 with a(1,1)=0:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..2..2....0..2..0....0..2..0....0..2..2....0..2..0....0..2..0....0..2..0
..2..0..1....0..1..3....0..2..1....0..3..2....0..1..0....0..3..2....0..2..3
..0..1..3....2..2..2....1..2..2....3..0..3....3..2..3....0..3..3....0..2..3
..3..3..0....1..2..0....3..3..3....0..3..1....0..1..0....3..1..0....1..1..3

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A185567.

Empirical: a(n) = 57*a(n-1) - 45*a(n-2).

Empirical g.f.: 4*x*(4 - 3*x) / (1 - 57*x + 45*x^2). - Colin Barker, Apr 16 2018

A185562 1/4 the number of n X 4 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

64, 13500, 2842560, 598507920, 126017211780, 26533211918040, 5586628402633500, 1176277376648694960, 247667889663690066720, 52147040135402715629580, 10979678466093753927519840, 2311796391622216326875508300

Offset: 1

R. H. Hardin, Jan 31 2011

nonn

Column 4 of A185567.

			Some solutions for 3 X 4 with a(1,1)=0:
..0..0..2..0....0..0..3..0....0..2..0..2....0..0..3..1....0..2..2..0
..0..2..0..3....2..0..3..2....0..2..0..2....2..2..2..2....0..2..0..2
..0..3..3..2....2..2..1..2....2..3..2..1....0..3..0..0....0..2..3..2

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A185567.

Empirical: a(n) = 217*a(n-1) - 1371*a(n-2) + 2835*a(n-3) - 2025*a(n-4).

Empirical g.f.: 4*x*(16 - 97*x + 201*x^2 - 135*x^3) / (1 - 217*x + 1371*x^2 - 2835*x^3 + 2025*x^4). - Colin Barker, Apr 16 2018

A185563 1/4 the number of n X 5 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

256, 202500, 159749820, 126017211780, 99407416968000, 78416544382742160, 61858104930689319360, 48796145962555619907720, 38492350573406180494467240, 30364304873646611423433030660, 23952577505016018447231455650500

Offset: 1

R. H. Hardin, Jan 31 2011

nonn

Column 5 of A185567.

			Some solutions for 3 X 5 with a(1,1)=0.
..0..0..0..2..3....0..0..0..3..0....0..0..2..2..1....0..0..0..0..2
..0..2..2..0..0....0..2..0..0..1....0..2..0..1..2....0..2..2..0..1
..0..0..3..2..0....0..0..1..3..1....0..0..2..1..2....0..2..3..3..1

R. H. Hardin, Table of n, a(n) for n = 1..169

Cf. A185567.

Empirical: a(n) = 829*a(n-1)-32339*a(n-2)+525706*a(n-3)-4547088*a(n-4)+22231638*a(n-5)-58780485*a(n-6)+68179725*a(n-7)-10661625*a(n-8).

A185564 1/4 the number of nX6 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

1024, 3037500, 8977824540, 26533211918040, 78416544382742160, 231753101877188629380, 684925618712729136913980, 2024236566241727245692157080, 5982450596328307878990974438640

Offset: 1

R. H. Hardin Jan 31 2011

nonn

Column 6 of A185567

			Some solutions for 3X6 with a(1,1)=0
..0..0..0..2..2..2....0..0..0..2..0..0....0..0..0..0..0..3....0..0..0..2..2..3
..0..2..2..0..1..0....0..2..0..2..2..1....0..2..2..2..0..2....0..2..0..2..0..3
..0..0..2..2..2..2....0..0..2..3..0..0....0..0..0..2..3..2....0..0..2..3..1..3

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=3176*a(n-1)-673550*a(n-2)+65136330*a(n-3)-3727689126*a(n-4)+139845804688*a(n-5)-3603160371660*a(n-6)+64834978133874*a(n-7)-810096692648238*a(n-8)+6824155175157060*a(n-9)-36345608355460626*a(n-10)+107463532615201134*a(n-11)-134880780658290660*a(n-12)+77768725332170250*a(n-13)-12154766339477250*a(n-14)-11593534218480000*a(n-15)+6932136333037500*a(n-16)-1023032228765625*a(n-17)

A185566 1/4 the number of nX8 0..3 arrays with no element equal both to the element above and to the element to its left.

Original entry on oeis.org

16384, 683437500, 28355191537860, 1176277376648694960, 48796145962555619907720, 2024236566241727245692157080, 83972485690826213759616527499540, 3483475434832751291309593655505225600

Offset: 1

R. H. Hardin Jan 31 2011

nonn

Column 8 of A185567

			Some solutions for 3X8 with a(1,1)=0
..0..0..0..0..0..0..1..3....0..0..0..0..0..0..1..1....0..0..0..0..0..2..2..1
..0..2..0..2..2..0..0..1....0..2..0..2..2..2..3..1....0..2..0..2..2..0..2..3
..0..0..2..0..0..2..0..3....0..0..2..0..0..2..2..1....0..0..2..0..2..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..158

cp's OEIS Frontend

A185565 1/4 the number of nX7 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185560 1/4 the number of n X n 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185561 1/4 the number of n X 3 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185562 1/4 the number of n X 4 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185563 1/4 the number of n X 5 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185564 1/4 the number of nX6 0..3 arrays with no element equal both to the element above and to the element to its left.

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A185566 1/4 the number of nX8 0..3 arrays with no element equal both to the element above and to the element to its left.

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