cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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.

Original entry on oeis.org

4096, 45562500, 504547256880, 5586628402633500, 61858104930689319360, 684925618712729136913980, 7583858300260627032845531520, 83972485690826213759616527499540, 929787724653148422947168982361958940
Offset: 1

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Author

R. H. Hardin Jan 31 2011

Keywords

Comments

Column 7 of A185567

Examples

			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
		

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

Views

Author

R. H. Hardin Jan 31 2011

Keywords

Comments

Diagonal of A185567

Examples

			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
		

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

Views

Author

R. H. Hardin, Jan 31 2011

Keywords

Comments

Column 3 of A185567.

Examples

			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
		

Crossrefs

Cf. A185567.

Formula

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

Views

Author

R. H. Hardin, Jan 31 2011

Keywords

Comments

Column 4 of A185567.

Examples

			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
		

Crossrefs

Cf. A185567.

Formula

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

Views

Author

R. H. Hardin, Jan 31 2011

Keywords

Comments

Column 5 of A185567.

Examples

			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
		

Crossrefs

Cf. A185567.

Formula

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

Views

Author

R. H. Hardin Jan 31 2011

Keywords

Comments

Column 6 of A185567

Examples

			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
		

Formula

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

Views

Author

R. H. Hardin Jan 31 2011

Keywords

Comments

Column 8 of A185567

Examples

			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
		
Showing 1-7 of 7 results.