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.

A206694 Number of n X 2 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

9, 81, 676, 5625, 46656, 386884, 3207681, 26594649, 220492801, 1828075536, 15156318321, 125658906256, 1041820324416, 8637585806529, 71613009227809, 593733388556025, 4922560027477764, 40812252925262329, 338368649551172496
Offset: 1

Views

Author

R. H. Hardin, Feb 11 2012

Keywords

Comments

Column 2 of A206700.

Examples

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

Crossrefs

Cf. A206700.

Formula

Empirical: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6).
Empirical g.f.: x*(9 - 26*x^2 + 9*x^3 + 3*x^4 - x^5) / ((1 - 9*x + 6*x^2 - x^3)*(1 - 3*x^2 - x^3)). - Colin Barker, Feb 23 2018

A206693 Number of n X n 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

3, 81, 15712, 23335217, 262482902920, 22540704363210913, 14777630573426014735558, 74010398585294927963749126971, 2831737193779046594636895038867701496
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Diagonal of A206700

Examples

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

A206695 Number of nX3 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

26, 676, 15712, 363465, 8366690, 192513201, 4428597297, 101873060353, 2343406014665, 53905733689480, 1240001271788197, 28523922980667486, 656139776848417214, 15093274671338487633, 347192698846268632122
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Column 3 of A206700

Examples

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

Formula

Empirical: a(n) = 29*a(n-1) -84*a(n-2) -1570*a(n-3) +6618*a(n-4) +28026*a(n-5) -136815*a(n-6) -145173*a(n-7) +1005714*a(n-8) -486446*a(n-9) -1842056*a(n-10) +1805556*a(n-11) +1069186*a(n-12) -1763040*a(n-13) +27675*a(n-14) +626313*a(n-15) -148782*a(n-16) -66294*a(n-17) +19454*a(n-18) +2708*a(n-19) -849*a(n-20) -37*a(n-21) +12*a(n-22)

A206696 Number of nX4 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

75, 5625, 363465, 23335217, 1488199144, 94853765621, 6043775871265, 385074186960645, 24534288457459085, 1563152762306175249, 99593046497034263129, 6345364097458333024131, 404281676173244236904185
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Column 4 of A206700

Examples

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

Formula

Empirical: a(n) = 78*a(n-1) -234*a(n-2) -51844*a(n-3) +367977*a(n-4) +14226694*a(n-5) -107162723*a(n-6) -2058590883*a(n-7) +14245169702*a(n-8) +166850830601*a(n-9) -1006522155710*a(n-10) -7705612288607*a(n-11) +41742029532952*a(n-12) +224178262145763*a(n-13) -1117135706465069*a(n-14) -4432691211165410*a(n-15) +20614240005494274*a(n-16) +62538652868703498*a(n-17) -273860843124418175*a(n-18) -648624786200303292*a(n-19) +2692512356078627392*a(n-20) +5030941296219548542*a(n-21) -19920980073167801034*a(n-22) -29421781424500467014*a(n-23) +111901842534836226859*a(n-24) +129940242928625276061*a(n-25) -478648989222923058240*a(n-26) -432032846450905336578*a(n-27) +1556871771824961527184*a(n-28) +1075290642349862467282*a(n-29) -3835989284955950430237*a(n-30) -1993419911070741060429*a(n-31) +7133520058817141306429*a(n-32) +2752192782196085648447*a(n-33) -10010143200461873707530*a(n-34) -2850031694840912727487*a(n-35) +10653341981028939089343*a(n-36) +2237306838293672561239*a(n-37) -8669055168975544431574*a(n-38) -1344810876350142753928*a(n-39) +5438572582878463592631*a(n-40) +623294425944545086565*a(n-41) -2647317893533182049909*a(n-42) -223380392780838930930*a(n-43) +1003321113825970315629*a(n-44) +61787295202194182549*a(n-45) -296035972064257500351*a(n-46) -13099235661806084050*a(n-47) +67718125251587003177*a(n-48) +2102420535402354027*a(n-49) -11902839260661902107*a(n-50) -250860988208440654*a(n-51) +1584324118158827169*a(n-52) +21727207565065182*a(n-53) -156279332999084303*a(n-54) -1328513806559874*a(n-55) +11084056047152363*a(n-56) +55910412332260*a(n-57) -543227737584804*a(n-58) -1596333995574*a(n-59) +17568605766252*a(n-60) +30221533209*a(n-61) -359729286568*a(n-62) -347623271*a(n-63) +4430212480*a(n-64) +2101680*a(n-65) -29714112*a(n-66) -5184*a(n-67) +82944*a(n-68)

A206697 Number of nX5 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

216, 46656, 8366690, 1488199144, 262482902920, 46260684361347, 8149739471342829, 1435662206447144342, 252901661556478734640, 44550197492083630730323, 7847785175617092397593472
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Column 5 of A206700

Examples

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

A206698 Number of nX6 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

622, 386884, 192513201, 94853765621, 46260684361347, 22540704363210913, 10977508218092030949, 5345785254841179750528, 2603202653456919727333824, 1267659520116049754553214784, 617300558095977800421783249695
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Column 6 of A206700

Examples

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

A206699 Number of nX7 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.

Original entry on oeis.org

1791, 3207681, 4428597297, 6043775871265, 8149739471342829, 10977508218092030949, 14777630573426014735558, 19891697466939518338949937, 26774752595905814904083950218, 36039345751281018973667189182614
Offset: 1

Views

Author

R. H. Hardin Feb 11 2012

Keywords

Comments

Column 7 of A206700

Examples

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