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 1-6 of 6 results.

A206989 Number of n X 3 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

7, 49, 174, 840, 3858, 17460, 80070, 365784, 1670838, 7636416, 34893438, 159444240, 728589330, 3329288484, 15213221238, 69517022592, 317658800982, 1451545657152, 6632855083422, 30308909178984, 138496917825186, 632863297956804
Offset: 1

Views

Author

R. H. Hardin, Feb 14 2012

Keywords

Comments

Column 3 of A206994.

Examples

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

Crossrefs

Cf. A206994.

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7) for n>9.
Empirical g.f.: x*(1 - x)*(7 + 35*x + 27*x^2 + 23*x^3 - 13*x^4 - 3*x^5 - x^6 + x^7) / (1 - 3*x - 5*x^2 - 11*x^3 + 5*x^4 - x^5 + 3*x^6 - x^7). - Colin Barker, Jun 17 2018

A206990 Number of nX4 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

13, 169, 840, 6510, 46878, 329952, 2371090, 16939450, 120961040, 864671390, 6178621414, 44150290200, 315500062138, 2254527357770, 16110599565656, 115124947986150, 822671737926942, 5878731842796456, 42008857944366290
Offset: 1

Views

Author

R. H. Hardin Feb 14 2012

Keywords

Comments

Column 4 of A206994

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +17*a(n-2) +135*a(n-3) +74*a(n-4) -7*a(n-5) -1496*a(n-6) +492*a(n-7) -890*a(n-8) +4192*a(n-9) -1374*a(n-10) +1082*a(n-11) -3316*a(n-12) +622*a(n-13) +112*a(n-14) +684*a(n-15) -125*a(n-16) -42*a(n-17) -43*a(n-18) +7*a(n-19) +2*a(n-20) +a(n-21) for n>23

A206991 Number of nX5 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

24, 576, 3858, 46878, 516724, 5517786, 60684900, 661767626, 7210995166, 78708157668, 858531177576, 9365112576008, 102166147775280, 1114491009075716, 12157784157741082, 132627063247482110, 1446796068890738540
Offset: 1

Views

Author

R. H. Hardin Feb 14 2012

Keywords

Comments

Column 5 of A206994

Examples

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

Formula

Empirical: a(n) = a(n-1) +28*a(n-2) +875*a(n-3) +802*a(n-4) +2824*a(n-5) -131139*a(n-6) +34873*a(n-7) -770465*a(n-8) +9266365*a(n-9) -11531301*a(n-10) +56876379*a(n-11) -355076183*a(n-12) +544384223*a(n-13) -1672404915*a(n-14) +7154271457*a(n-15) -10209145829*a(n-16) +22701111393*a(n-17) -77873418461*a(n-18) +93554028359*a(n-19) -154165003455*a(n-20) +483619402367*a(n-21) -468861781375*a(n-22) +537519134381*a(n-23) -1826906434245*a(n-24) +1437081052785*a(n-25) -898560316329*a(n-26) +4448071983175*a(n-27) -3045677327539*a(n-28) +288542513915*a(n-29) -7146694039935*a(n-30) +4753142608517*a(n-31) +1461892127469*a(n-32) +7666175656799*a(n-33) -5408808370873*a(n-34) -2784446755743*a(n-35) -5581405898903*a(n-36) +4327845773467*a(n-37) +2523233043991*a(n-38) +2834217077963*a(n-39) -2368693334243*a(n-40) -1394941028489*a(n-41) -1042798666831*a(n-42) +869497890385*a(n-43) +503785545915*a(n-44) +288501740701*a(n-45) -208579544409*a(n-46) -120110482461*a(n-47) -60150849143*a(n-48) +31305217451*a(n-49) +18409190089*a(n-50) +8950155437*a(n-51) -2723100941*a(n-52) -1703968227*a(n-53) -857046549*a(n-54) +126357391*a(n-55) +90444937*a(n-56) +49032475*a(n-57) -2724387*a(n-58) -2624435*a(n-59) -1601649*a(n-60) +19273*a(n-61) +40011*a(n-62) +29047*a(n-63) +48*a(n-64) -300*a(n-65) -271*a(n-66) +a(n-68) +a(n-69) for n>71

A206992 Number of nX6 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

44, 1936, 17460, 329952, 5517786, 88819714, 1482397764, 24487141408, 404028674322, 6680807680870, 110384929625108, 1823827049092968, 30138255315895530, 497995973048057786, 8228770269287650676
Offset: 1

Views

Author

R. H. Hardin Feb 14 2012

Keywords

Comments

Column 6 of A206994

Examples

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

A206993 Number of nX7 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

81, 6561, 80070, 2371090, 60684900, 1482397764, 37849652838, 954576893140, 24031904480250, 606711286710758, 15303296459686032, 385968153194641688, 9736392679516458222, 245594233526815556440, 6194918451958959626262
Offset: 1

Views

Author

R. H. Hardin Feb 14 2012

Keywords

Comments

Column 7 of A206994

Examples

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

A206988 Number of n X n 0..1 arrays avoiding 0 0 0 horizontally and 1 1 1 vertically.

Original entry on oeis.org

2, 16, 174, 6510, 516724, 88819714, 37849652838, 36679559167444, 82039130470188394, 429029852979061855882, 5194153238714571994969836, 145816870651378340099973452074
Offset: 1

Views

Author

R. H. Hardin Feb 14 2012

Keywords

Comments

Diagonal of A206994

Examples

			Some solutions for n=4
..1..1..1..1....1..0..1..0....1..0..0..1....1..0..1..0....0..1..0..1
..1..1..0..1....1..1..0..1....0..1..1..0....1..0..0..1....1..1..1..0
..0..0..1..0....0..1..0..0....1..0..1..1....0..1..0..0....0..0..1..0
..1..1..1..0....1..0..1..0....1..1..0..1....0..1..0..0....0..1..0..1
		
Showing 1-6 of 6 results.