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.

A209013 Number of n X 2 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

12, 130, 1430, 15724, 172936, 1901964, 20918008, 230058424, 2530206824, 27827480224, 306049553920, 3365965156848, 37019238613696, 407141477256160, 4477784761704800, 49247147465796160, 541625304181537792
Offset: 1

Views

Author

R. H. Hardin, Mar 04 2012

Keywords

Comments

Column 2 of A209019.

Examples

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

Crossrefs

Cf. A209019.

Formula

Empirical: a(n) = 8*a(n-1) + 38*a(n-2) - 52*a(n-3) - 40*a(n-4) + 44*a(n-5) - 12*a(n-6).
Empirical g.f.: 2*x*(6 + 17*x - 33*x^2 - 16*x^3 + 22*x^4 - 2*x^5) / (1 - 8*x - 38*x^2 + 52*x^3 + 40*x^4 - 44*x^5 + 12*x^6). - Colin Barker, Jul 07 2018

A209014 Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

36, 1430, 57412, 2303052, 92409982, 3707858104, 148774643618, 5969451726624, 239519039453858, 9610491871316864, 385612583729466606, 15472367675895217344, 620815222721162751908, 24909667900333112532040
Offset: 1

Views

Author

R. H. Hardin, Mar 04 2012

Keywords

Comments

Column 3 of A209019.

Examples

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

Crossrefs

Cf. A209019.

Formula

Empirical: a(n) = 30*a(n-1) +507*a(n-2) -3690*a(n-3) -16906*a(n-4) +106528*a(n-5) +124733*a(n-6) -1050424*a(n-7) +577820*a(n-8) +3131188*a(n-9) -4615763*a(n-10) -850984*a(n-11) +5888706*a(n-12) -4406256*a(n-13) +1242404*a(n-14) -133476*a(n-15) +1080*a(n-16) +864*a(n-17).

A209015 Number of nX4 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

108, 15724, 2303052, 337083370, 49349902246, 7224768704460, 1057701934285612, 154846841369187254, 22669475693064075854, 3318796151990660980412, 485869556318230056701646, 71130980457981221221106644
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 4 of A209019

Examples

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

Formula

Empirical: a(n) = 121*a(n-1) +5730*a(n-2) -286920*a(n-3) -2230550*a(n-4) +168111699*a(n-5) -294889621*a(n-6) -40576917506*a(n-7) +278469929272*a(n-8) +4185653952679*a(n-9) -51679493388906*a(n-10) -95521480620954*a(n-11) +3917029561300381*a(n-12) -12619545022627596*a(n-13) -116519992699014814*a(n-14) +921470247221265689*a(n-15) -119314240369267058*a(n-16) -21755424443481809339*a(n-17) +76040536569580318461*a(n-18) +114661181811939421726*a(n-19) -1357725604456162658889*a(n-20) +2421087559015872647850*a(n-21) +6149428808328956427545*a(n-22) -30883693864978949164736*a(n-23) +21715521985680502773934*a(n-24) +121577848721422211358097*a(n-25) -282515614398015795553233*a(n-26) -59401783650000309680112*a(n-27) +975489045665324929868215*a(n-28) -948722481222129857685702*a(n-29) -1327450811491294031946559*a(n-30) +3197130081855174858692241*a(n-31) -375821449794905094130651*a(n-32) -4691721934473468324109304*a(n-33) +3863156809522165838208261*a(n-34) +3153863823478852306299581*a(n-35) -5996729276936836482160104*a(n-36) +207065725654100689193478*a(n-37) +5011502450288579874906392*a(n-38) -2360115036652008244193773*a(n-39) -2514469390051829479202967*a(n-40) +2374772123540643629418123*a(n-41) +628695226019219665423080*a(n-42) -1378444535051876357809410*a(n-43) +82722580096724428234311*a(n-44) +530121626682994473729220*a(n-45) -138965847696073156085105*a(n-46) -138249556554994118098499*a(n-47) +61438878901505761010146*a(n-48) +21473460220917979164857*a(n-49) -16472927063957604369756*a(n-50) +476472768687994672934*a(n-51) +2374787095197934792127*a(n-52) -1417255222031476419249*a(n-53) +362528775484506288419*a(n-54) +258759203906273804423*a(n-55) -218812945298855222271*a(n-56) +6317554856819353548*a(n-57) +31688055162233226837*a(n-58) -765235142583070563*a(n-59) -3374058137343271254*a(n-60) -559617723065314773*a(n-61) +314957827294734249*a(n-62) +51896030974806510*a(n-63) -2493656515165842*a(n-64) -6141332967576516*a(n-65) +509451270235560*a(n-66) +49818992233392*a(n-67) -1091729194848*a(n-68) -79830468864*a(n-69)

A209016 Number of nX5 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

324, 172936, 92409982, 49349902246, 26361689168962, 14081479775124768, 7521858792951566188, 4017924265572698697072, 2146240525684764881824534, 1146449720400141412616571132, 612395008605837895502174401436
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 5 of A209019

Examples

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

A209017 Number of nX6 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

972, 1901964, 3707858104, 7224768704460, 14081479775124768, 27444816617702590210, 53490209804089514438574, 104252853354306374638934760, 203189693440653459494447382012
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 6 of A209019

Examples

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

A209018 Number of nX7 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

2916, 20918008, 148774643618, 1057701934285612, 7521858792951566188, 53490209804089514438574, 380386826513820237531618354, 2705056288752965649168385141630, 19236551636169391849856640820638184
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Column 7 of A209019

Examples

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

A209012 Number of n X n 0..3 arrays with no element equal the average of immediate neighbors vertically above, diagonally above and left, and horizontally left of it.

Original entry on oeis.org

4, 130, 57412, 337083370, 26361689168962, 27444816617702590210, 380386826513820237531618354, 70188235698940395931354096660136964, 172416055686564260854366909730038107238333862
Offset: 1

Views

Author

R. H. Hardin Mar 04 2012

Keywords

Comments

Diagonal of A209019

Examples

			Some solutions for n=4
..2..3..1..0....1..2..1..3....2..3..1..3....1..3..2..1....0..1..2..3
..3..2..3..0....3..3..3..0....3..2..1..1....2..1..0..3....1..3..3..0
..2..3..3..0....0..3..1..1....0..2..0..1....3..3..3..0....2..0..1..2
..1..3..0..2....3..1..0..0....1..3..3..1....0..3..1..3....1..2..0..0
		
Showing 1-7 of 7 results.