A283042 -id:A283042 - cp's OEIS frontend

A283036 Number of n X 2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

0, 4, 16, 68, 256, 924, 3232, 11044, 37104, 122984, 403280, 1310760, 4228960, 13558932, 43239776, 137251068, 433883696, 1366668772, 4290998336, 13433966724, 41949331616, 130685405648, 406258440928, 1260465716560, 3903760205760

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Column 2 of A283042.

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

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

Cf. A283042.

Empirical: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8).

Empirical: G.f.: -4*x^2*(x-1)*(1+x)/(x^4-3*x^2-2*x+1)^2. - R. J. Mathar, Mar 02 2017

A283037 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

1, 16, 119, 818, 5065, 30378, 175963, 997302, 5559013, 30578068, 166427637, 897975464, 4809947903, 25605505484, 135587794041, 714668815274, 3751742509465, 19624971865578, 102330051488077, 532058283113570

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Column 3 of A283042.

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

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

Cf. A283042.

Empirical: a(n) = 4*a(n-1) +16*a(n-2) -154*a(n-4) -470*a(n-5) -644*a(n-6) -306*a(n-7) +401*a(n-8) +700*a(n-9) +315*a(n-10) -82*a(n-11) -168*a(n-12) -104*a(n-13) -11*a(n-14) +14*a(n-15) +5*a(n-16) +2*a(n-17) -a(n-18)

A283038 Number of nX4 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

2, 68, 818, 9152, 94368, 931844, 8912378, 83420984, 767704036, 6973000128, 62669779812, 558371394860, 4938938283902, 43417600038648, 379661067157816, 3304658457345168, 28648616561102224, 247474652799713212

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Column 4 of A283042.

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

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

Cf. A283042.

Empirical: a(n) = 8*a(n-1) +38*a(n-2) -98*a(n-3) -1221*a(n-4) -3374*a(n-5) -1845*a(n-6) +8406*a(n-7) +14610*a(n-8) -5894*a(n-9) -20336*a(n-10) +9134*a(n-11) +9660*a(n-12) -7192*a(n-13) +3651*a(n-14) -16004*a(n-15) +9859*a(n-16) +3230*a(n-17) -14482*a(n-18) +15860*a(n-19) -16472*a(n-20) +13768*a(n-21) -9574*a(n-22) +4838*a(n-23) -2040*a(n-24) +772*a(n-25) -272*a(n-26) +84*a(n-27) -16*a(n-28) +4*a(n-29) -a(n-30)

A283039 Number of n X 5 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

5, 256, 5065, 94368, 1604067, 26180826, 414085368, 6406597648, 97480211225, 1463896864692, 21753273510360, 320461563276470, 4686814034042643, 68124911104620870, 984999389958209910, 14176505420268232960, 203212970311422645415, 2902589960282552892838, 41327736536350218694304

Offset: 1

R. H. Hardin, Feb 27 2017

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 72

Column 5 of A283042.

Empirical recurrence of order 72 (see link above).

A283040 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

12, 924, 30378, 931844, 26180826, 706205768, 18455711930, 471954803540, 11868995624930, 294610925837548, 7236339162353190, 176211017312981820, 4259949495613038410, 102354621908646110164, 2446336908511893682666

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Column 6 of A283042.

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

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

Cf. A283042.

A283041 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

26, 3232, 175963, 8912378, 414085368, 18455711930, 797350288363, 33705434438284, 1401215705047092, 57496998569457406, 2334654228770351159, 93982808773859979206, 3756077506881552506247, 149195064747909416762172

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Column 7 of A283042.

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

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

Cf. A283042.

A283035 Number of n X n 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

Original entry on oeis.org

0, 4, 119, 9152, 1604067, 706205768, 797350288363, 2355217281173760, 18388049679475271526, 382245292023510825419744

Offset: 1

R. H. Hardin, Feb 27 2017

nonn

Diagonal of A283042.

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

Cf. A283042.

cp's OEIS Frontend

A283036 Number of n X 2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283037 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283038 Number of nX4 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283039 Number of n X 5 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283040 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283041 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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A283035 Number of n X n 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

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