A268995 -id:A268995 - cp's OEIS frontend

A268992 Number of nX5 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

23, 278, 3331, 37987, 421450, 4583103, 49084071, 519385102, 5442503771, 56571775611, 584048456162, 5994862809815, 61225907059807, 622579765715526, 6306473266306611, 63664757730483923, 640753995659371194

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 5 of A268995.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268995.

Empirical: a(n) = 26*a(n-1) -241*a(n-2) +994*a(n-3) -2060*a(n-4) +2218*a(n-5) -1201*a(n-6) +290*a(n-7) -25*a(n-8) for n>9

A268988 Number of n X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

2, 13, 174, 6009, 421450, 66954420, 22995344760, 17373640598542, 29082748697180602, 107300241515211644436, 883523091936988991189604, 16140842052133986432421342048, 659806253617230823177640504040304

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Diagonal of A268995.

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

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A268995.

A268989 Number of n X 2 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

4, 13, 41, 126, 379, 1121, 3272, 9449, 27049, 76866, 217079, 609793, 1705036, 4748101, 13174889, 36440646, 100503667, 276476129, 758785424, 2078056481, 5680052329, 15497929098, 42216552431, 114824352001, 311871557524

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 2 of A268995.

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

Empirical g.f.: x*(4 - 11*x + 7*x^2 - x^3) / (1 - 3*x + x^2)^2. - Colin Barker, Jan 17 2019

A268990 Number of n X 3 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

7, 35, 174, 849, 4083, 19416, 91491, 427863, 1988142, 9187653, 42256599, 193542240, 883204143, 4017241083, 18219040206, 82410172617, 371879874987, 1674499435176, 7525052043819, 33755742643791, 151168877259918, 675941817039645

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A268995.

Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3) - 9*a(n-4).

Empirical g.f.: x*(7 - 35*x + 41*x^2 - 16*x^3) / (1 - 5*x + 3*x^2)^2. - Colin Barker, Jan 17 2019

A268991 Number of n X 4 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

13, 103, 805, 6009, 43512, 308112, 2144780, 14730784, 100087792, 674045392, 4505925696, 29933341056, 197782652096, 1300744853760, 8519586895104, 55600022810880, 361688403251200, 2346083095244800, 15178387509332992

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 4 of A268995.

Empirical: a(n) = 16*a(n-1) - 88*a(n-2) + 200*a(n-3) - 208*a(n-4) + 96*a(n-5) - 16*a(n-6) for n>7.

Empirical g.f.: x*(13 - 105*x + 301*x^2 - 407*x^3 + 312*x^4 - 112*x^5 + 4*x^6) / (1 - 8*x + 12*x^2 - 4*x^3)^2. - Colin Barker, Jan 17 2019

A268993 Number of nX6 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

41, 763, 14080, 244397, 4097199, 66954420, 1073436321, 16957258387, 264744926212, 4093941136805, 62806688095479, 957111538353668, 14502245681077257, 218656000387543867, 3282569954305098964

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 6 of A268995.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268995.

Empirical: a(n) = 42*a(n-1) -665*a(n-2) +5138*a(n-3) -21972*a(n-4) +55274*a(n-5) -83769*a(n-6) +76202*a(n-7) -40273*a(n-8) +11304*a(n-9) -1296*a(n-10) for n>12

A268994 Number of nX7 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

72, 2037, 57287, 1506570, 38241770, 946498448, 22995344760, 550731432312, 13040291111728, 305911647779632, 7121104059933536, 164688437285444064, 3787495455529375808, 86684333527271203264, 1975573336154420926848

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Column 7 of A268995.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268995.

Empirical: a(n) = 68*a(n-1) -1804*a(n-2) +24560*a(n-3) -195400*a(n-4) +974752*a(n-5) -3171360*a(n-6) +6871936*a(n-7) -9999248*a(n-8) +9740096*a(n-9) -6250176*a(n-10) +2552576*a(n-11) -621824*a(n-12) +79872*a(n-13) -4096*a(n-14) for n>16

A268996 Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

4, 13, 35, 103, 278, 763, 2037, 5421, 14264, 37321, 97015, 250963, 646250, 1657719, 4237481, 10798553, 27442092, 69563653, 175938699, 444060607, 1118668286, 2813233523, 7063416349, 17708464645, 44335423456, 110857865665, 276863340767

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 2 of A268995.

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 4*a(n-3) - 11*a(n-4) - 6*a(n-5) - a(n-6).

Empirical g.f.: x*(4 + 5*x - 11*x^2 - 16*x^3 - 7*x^4 - x^5) / ((1 + x)^2*(1 - 2*x - x^2)^2). - Colin Barker, Jan 18 2019

A268997 Number of 3 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

8, 41, 174, 805, 3331, 14080, 57287, 232449, 928886, 3688159, 14524152, 56872865, 221485093, 858684462, 3315594029, 12757162785, 48929395140, 187135343189, 713890088738, 2717075148077, 10319450344743, 39117842242220

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 3 of A268995.

Empirical: a(n) = 3*a(n-1) + 12*a(n-2) - 16*a(n-3) - 62*a(n-4) - 34*a(n-5) + 16*a(n-6) + 12*a(n-7) - a(n-8) - a(n-9).

Empirical g.f.: x*(8 + 17*x - 45*x^2 - 81*x^3 - 20*x^4 + 25*x^5 + 9*x^6 - 2*x^7 - x^8) / ((1 + x)*(1 - 2*x - 6*x^2 + x^4)^2). - Colin Barker, Jan 18 2019

A268998 Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

16, 126, 849, 6009, 37987, 244397, 1506570, 9258784, 55904997, 335264275, 1991983545, 11763490813, 69051103048, 403375829894, 2346089237885, 13593697842329, 78497992061491, 451930855824889, 2594820580805818

Offset: 1

R. H. Hardin, Feb 17 2016

nonn

Row 4 of A268995.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268995.

Empirical: a(n) = 2*a(n-1) +39*a(n-2) +14*a(n-3) -482*a(n-4) -1102*a(n-5) -111*a(n-6) +1758*a(n-7) +982*a(n-8) -1114*a(n-9) -743*a(n-10) +394*a(n-11) +206*a(n-12) -90*a(n-13) -17*a(n-14) +10*a(n-15) -a(n-16)

cp's OEIS Frontend

A268992 Number of nX5 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268988 Number of n X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A268989 Number of n X 2 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268990 Number of n X 3 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268991 Number of n X 4 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268993 Number of nX6 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268994 Number of nX7 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268996 Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268997 Number of 3 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268998 Number of 4Xn binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

Views

Author

Keywords