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 1-10 of 13 results. Next

A231833 Number of n X 2 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

4, 50, 422, 3823, 34350, 308419, 2771101, 24892609, 223618304, 2008825312, 18045827096, 162110668160, 1456284886944, 13082209530648, 117521102664489, 1055724534522884, 9483865176690522, 85196181144951446, 765340833781554407
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Examples

			Some solutions for n=7:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..2..2....2..2....0..0....0..0....0..0....2..0....0..2....0..0....0..0....2..0
..2..3....2..3....1..0....0..0....2..0....0..0....0..0....0..0....0..3....0..0
..3..3....2..2....0..0....1..3....0..2....3..1....3..2....0..1....0..0....0..0
..2..2....3..1....1..3....2..2....2..2....1..1....2..2....2..2....1..3....3..2
..1..0....1..1....2..2....2..1....3..2....3..3....3..1....3..3....0..0....2..2
..0..1....3..3....0..0....1..1....1..1....0..0....1..3....2..2....0..3....1..1
		

Crossrefs

Column 2 of A231839.

Formula

Empirical: a(n) = 4*a(n-1) + 34*a(n-2) + 86*a(n-3) + 91*a(n-4) + 46*a(n-5) + 11*a(n-6) + a(n-7).
Empirical g.f.: x*(2 + x)*(2 + 4*x + x^2)*(1 + 6*x + 5*x^2 + x^3) / (1 - 4*x - 34*x^2 - 86*x^3 - 91*x^4 - 46*x^5 - 11*x^6 - x^7). - Colin Barker, Oct 01 2018

A231834 Number of nX3 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

16, 188, 4508, 111621, 2836554, 71178861, 1792092360, 45099279326, 1134900171250, 28560684486812, 718739864735561, 18087411635523189, 455177754069590473, 11454748470680974894, 288263810554257272575
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Column 3 of A231839

Examples

			Some solutions for n=4
..1..0..0....3..0..0....2..1..1....0..0..0....2..2..3....3..2..1....3..1..0
..0..0..2....0..0..3....1..3..2....2..1..2....2..3..0....1..1..0....1..0..0
..0..1..2....2..2..2....3..1..1....0..0..1....1..0..0....0..0..1....0..0..3
..1..3..3....3..3..3....1..1..2....0..2..2....1..1..3....0..1..2....0..0..0
		

Formula

Empirical: a(n) = 16*a(n-1) +206*a(n-2) +762*a(n-3) -3181*a(n-4) -9838*a(n-5) +4473*a(n-6) +18193*a(n-7) +2848*a(n-8) -6404*a(n-9) -1848*a(n-10) for n>11

A231835 Number of nX4 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

50, 760, 52411, 3477361, 241961326, 16599585680, 1140658285204, 78428361897720, 5390322528656652, 370517687958114665, 25468098036554313595, 1750580722347118467767, 120328698088745644429376
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Column 4 of A231839

Examples

			Some solutions for n=3
..2..1..1..2....0..0..2..3....3..2..0..0....3..3..3..2....3..3..3..1
..1..0..0..0....0..2..1..1....0..0..0..1....2..1..1..1....0..0..0..0
..0..0..0..0....1..1..2..2....0..2..2..2....1..3..2..2....3..2..0..0
		

Formula

Empirical: a(n) = 50*a(n-1) +1285*a(n-2) +7390*a(n-3) -474257*a(n-4) -1804709*a(n-5) +26939722*a(n-6) +146411418*a(n-7) -723447888*a(n-8) -4625331556*a(n-9) +10015768057*a(n-10) +82892906609*a(n-11) -62795080068*a(n-12) -818760182586*a(n-13) -351667043000*a(n-14) +3018875872284*a(n-15) +2497051029141*a(n-16) -4738505166389*a(n-17) -4603655313597*a(n-18) +3261950222325*a(n-19) +3677474787541*a(n-20) -106455016254*a(n-21) -713820548139*a(n-22) -118783642889*a(n-23) +16718453115*a(n-24) +11208957796*a(n-25) +2071964480*a(n-26) +220038912*a(n-27) +12795904*a(n-28) +409600*a(n-29) for n>30

A231836 Number of nX5 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

144, 3309, 678660, 124132900, 24188209253, 4666623161419, 899426070636904, 173546274977761257, 33474310504831841795, 6456965889651937136227, 1245519756272860837583554, 240252847617486843960049416
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Column 5 of A231839

Examples

			Some solutions for n=2
..3..3..0..0..0....2..2..1..1..2....2..0..0..0..0....1..1..0..0..3
..0..0..3..2..2....2..1..1..1..1....0..0..0..1..2....3..0..0..2..2
		

Formula

Empirical recurrence of order 82 (see link above)

A231837 Number of nX6 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

422, 14666, 8887871, 4378313800, 2346558875473, 1254045703514371, 667414220139740867, 355666172689879084210, 189521117184760778293515, 100979609057565187903930604, 53805681791889243019883807740
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Column 6 of A231839

Examples

			Some solutions for n=2
..2..0..0..0..0..0....3..3..0..0..0..0....0..0..0..3..1..0....0..0..3..2..0..0
..0..0..3..1..1..3....0..0..0..0..3..3....0..0..0..0..0..0....0..1..1..0..0..2
		

A231838 Number of nX7 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

1268, 64607, 114873933, 150624159314, 220309043506362, 324616806882571299, 474822731471136470440, 695244971516001773033192, 1018294151929133028079374411, 1491192875210978136830040921123
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Column 7 of A231839

Examples

			Some solutions for n=2
..3..0..0..0..0..0..0....3..2..0..0..0..0..1....0..0..0..0..3..0..0
..0..0..2..1..0..0..0....1..0..0..0..0..1..3....3..3..0..0..0..0..3
		

A231840 Number of 2Xn 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

16, 50, 188, 760, 3309, 14666, 64607, 283479, 1243280, 5452114, 23905237, 104828007, 459770373, 2016638186, 8845269109, 38796696140, 170170211095, 746407664707, 3273942709889, 14360456936977, 62989372397071
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Row 2 of A231839

Examples

			Some solutions for n=5
..1..1..1..0..0....3..3..3..3..2....2..1..1..2..1....3..0..0..0..0
..2..1..0..0..1....2..2..2..2..3....1..1..1..1..2....0..1..1..1..2
		

Formula

Empirical: a(n) = 16*a(n-1) -120*a(n-2) +594*a(n-3) -2230*a(n-4) +6728*a(n-5) -16873*a(n-6) +35897*a(n-7) -65873*a(n-8) +105776*a(n-9) -149668*a(n-10) +188619*a(n-11) -211559*a(n-12) +213408*a(n-13) -191583*a(n-14) +154654*a(n-15) -110323*a(n-16) +68713*a(n-17) -37978*a(n-18) +15027*a(n-19) -6519*a(n-20) -1220*a(n-21) -499*a(n-22) -1885*a(n-23) -410*a(n-24) -615*a(n-25) -257*a(n-26) -118*a(n-27) -60*a(n-28) -15*a(n-29) -5*a(n-30) -a(n-31) for n>32

A231841 Number of 3Xn 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

64, 422, 4508, 52411, 678660, 8887871, 114873933, 1472320155, 18811450866, 240333888755, 3072777642636, 39304807956686, 502807539383400, 6431904732538361, 82273333965692552, 1052378549019652099
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Row 3 of A231839

Examples

			Some solutions for n=4
..3..3..2..0....3..2..2..1....3..2..1..0....1..1..1..3....2..2..3..0
..0..0..0..0....2..2..1..1....2..1..0..0....0..0..2..0....0..0..0..1
..3..3..1..1....3..3..2..2....3..3..1..1....0..0..0..1....2..3..2..2
		

A231842 Number of 4Xn 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

256, 3823, 111621, 3477361, 124132900, 4378313800, 150624159314, 5122053368703, 173935962002791, 5914591691652487, 201302640481651930, 6852837476350210815, 233279127016289974579, 7940697986290030781206, 270291946695181993650338
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Row 4 of A231839

Examples

			Some solutions for n=3
..0..0..0....2..1..0....2..2..0....2..2..2....0..0..0....2..1..1....1..1..0
..1..1..3....0..0..0....0..0..1....0..0..3....0..0..1....1..2..2....3..0..0
..1..1..0....3..3..1....2..3..2....0..1..1....0..2..0....3..3..1....3..3..2
..0..0..0....1..1..1....2..2..3....2..2..2....0..0..2....2..1..1....1..1..1
		

A231843 Number of 5Xn 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

Original entry on oeis.org

1024, 34350, 2836554, 241961326, 24188209253, 2346558875473, 220309043506362, 20436353978575810, 1898683544490465967, 176985535233028614945, 16519157344329121693878, 1541791797676344309156140
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2013

Keywords

Comments

Row 5 of A231839

Examples

			Some solutions for n=2
..1..1....1..1....2..1....0..0....3..3....2..2....0..0....3..3....0..0....3..0
..2..3....2..3....0..0....1..0....3..1....0..0....3..2....1..1....1..0....0..3
..1..1....3..2....2..1....0..3....1..2....2..2....2..0....1..2....0..0....2..0
..3..2....0..0....0..0....3..3....2..2....1..0....0..0....3..0....0..1....0..2
..2..2....1..1....0..3....0..0....2..2....0..2....1..1....0..0....1..1....2..2
		
Showing 1-10 of 13 results. Next