A282996 -id:A282996 - cp's OEIS frontend

A282990 Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

4, 11, 33, 98, 291, 865, 2570, 7637, 22693, 67432, 200373, 595405, 1769236, 5257255, 15621845, 46420050, 137936399, 409875693, 1217938738, 3619084505, 10754048825, 31955475472, 94955158681, 282157659273, 838426745764, 2491370993875

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 2 of A282996, A295275.

			Some solutions for n=5
..0..0. .1..1. .1..0. .0..0. .1..1. .1..0. .0..1. .1..0. .1..0. .0..0
..0..1. .0..0. .1..0. .1..0. .0..0. .0..0. .1..0. .1..0. .0..0. .0..1
..1..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..0. .0..0. .0..0. .0..0
..0..1. .0..0. .1..0. .1..0. .0..0. .0..0. .0..0. .0..0. .0..1. .0..0
..0..0. .0..0. .0..0. .1..0. .1..1. .0..1. .0..0. .1..1. .1..0. .1..1

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

Cf. A282996, A295275.

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

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

A282991 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

7, 33, 163, 803, 3971, 19587, 96693, 477297, 2355925, 11629027, 57401721, 283338413, 1398577069, 6903468049, 34075967931, 168201202963, 830252119477, 4098178655825, 20228877377719, 99851059281979, 492871346862069

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 3 of A282996.

			Some solutions for n=5
..0..0..1. .0..1..0. .0..0..0. .1..0..1. .0..1..0. .1..0..0. .1..0..0
..1..0..1. .0..1..0. .1..0..0. .0..0..1. .1..0..1. .0..0..1. .0..0..0
..0..0..0. .1..0..1. .0..1..0. .0..1..0. .1..0..0. .0..1..0. .0..1..0
..0..1..0. .1..0..1. .0..1..0. .0..1..0. .0..1..1. .0..1..0. .0..0..0
..1..0..0. .0..0..0. .1..0..1. .1..0..0. .0..0..0. .1..0..1. .0..0..1

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

Cf. A282996.

Empirical: a(n) = 2*a(n-1) +10*a(n-2) +20*a(n-3) +13*a(n-4) -9*a(n-5) -10*a(n-6) -3*a(n-7) -a(n-8) +a(n-9).

Empirical: G.f.: -x*(7+19*x+27*x^2+7*x^3-16*x^4-11*x^5-3*x^6+x^8) / ( (1+x)*(x^8-2*x^7-x^6-9*x^5+13*x^3+7*x^2+3*x-1) ). - R. J. Mathar, Mar 02 2017

A282992 Number of n X 4 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

13, 98, 803, 6547, 53389, 435027, 3546870, 28911809, 235681253, 1921212987, 15661161199, 127665372304, 1040691953095, 8483425185009, 69154476414585, 563727672983607, 4595348063993330, 37459973798636833, 305363079492664703, 2489233196683020273, 20291522858244231419

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 4 of A282996.

			Some solutions for n=5:
..0..0..1..0. .0..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..1
..0..0..1..0. .1..1..0..0. .0..0..0..1. .1..0..0..0. .0..0..1..0
..0..1..0..0. .0..0..1..1. .1..0..0..0. .0..0..0..1. .0..1..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..1. .1..1..0..1. .1..0..0..1
..1..1..0..1. .0..0..1..1. .1..1..0..1. .0..0..1..0. .0..0..0..0

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

Cf. A282996.

Empirical: a(n) = 4*a(n-1) +27*a(n-2) +59*a(n-3) -10*a(n-4) -134*a(n-5) +12*a(n-6) +43*a(n-7) -55*a(n-8) +42*a(n-9) -90*a(n-10) +58*a(n-11) -30*a(n-12) +6*a(n-13) -2*a(n-14) +a(n-15).

A282993 Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

24, 291, 3971, 53389, 720417, 9706901, 130854309, 1763845523, 23775564134, 320481684651, 4319920870201, 58230152122968, 784910642479634, 10580166410594089, 142614855902267366, 1922370270814992840

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 5 of A282996.

			Some solutions for n=5
..0..1..0..0..0. .1..0..0..0..1. .1..0..0..1..0. .1..0..0..0..0
..0..0..0..0..1. .0..0..1..0..0. .0..0..1..0..1. .0..0..0..0..1
..0..0..1..0..0. .0..0..0..0..0. .0..1..0..0..0. .0..0..0..0..1
..0..1..0..0..1. .1..0..0..0..1. .0..1..0..0..1. .1..0..1..1..0
..1..0..1..0..1. .0..1..0..0..0. .0..0..0..0..0. .0..0..0..0..1

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

Cf. A282996.

Empirical: a(n) = 5*a(n-1) +82*a(n-2) +424*a(n-3) +433*a(n-4) -3117*a(n-5) -9658*a(n-6) +8224*a(n-7) +43423*a(n-8) -39527*a(n-9) +4996*a(n-10) -8476*a(n-11) -208460*a(n-12) +596155*a(n-13) -915253*a(n-14) +1321254*a(n-15) -1511538*a(n-16) +1194611*a(n-17) -744475*a(n-18) +454071*a(n-19) -175360*a(n-20) +56609*a(n-21) -83755*a(n-22) -6781*a(n-23) +61170*a(n-24) -17072*a(n-25) -8350*a(n-26) -2485*a(n-27) +1059*a(n-28) +2774*a(n-29) -313*a(n-30) -159*a(n-31) -202*a(n-32) +69*a(n-33) +7*a(n-34) +a(n-35) -a(n-36)

A282994 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

44, 865, 19587, 435027, 9706901, 216173426, 4817792042, 107354061547, 2392171690343, 53305366529469, 1187812241964789, 26468219711250515, 589796016644509708, 13142526595924490676, 292857199578979575159

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 6 of A282996.

			Some solutions for n=5
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..1..1. .0..0..0..1..1..0
..0..0..0..1..0..1. .0..0..0..1..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0
..0..0..0..0..0..1. .0..0..0..1..0..0. .0..0..0..0..1..0. .0..0..0..0..0..1
..0..0..0..1..0..0. .0..0..0..0..0..0. .0..1..0..0..0..1. .0..1..1..0..0..1
..1..0..0..1..0..1. .1..0..0..0..1..0. .0..0..1..1..0..1. .1..0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 69

Cf. A282996.

Empirical recurrence of order 69 (see link above)

A282995 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

81, 2570, 96693, 3546870, 130854309, 4817792042, 177509416175, 6539125324144, 240894164469261, 8874303766960833, 326920126439954151, 12043397390708228297, 443666302338469244577, 16344206879501911050248

Offset: 1

R. H. Hardin, Feb 26 2017

nonn

Column 7 of A282996.

			Some solutions for n=5
..0..0..0..0..1..0..1. .0..0..0..0..1..0..1. .0..0..0..1..0..0..0
..0..0..0..1..0..0..0. .0..0..0..0..0..0..1. .0..0..0..0..1..0..0
..0..0..0..0..1..0..1. .0..0..1..1..0..0..0. .0..0..1..0..0..0..0
..0..0..0..0..1..0..0. .0..0..0..0..0..0..1. .0..0..0..0..1..0..1
..0..0..0..1..0..1..0. .0..0..0..0..1..1..0. .0..0..0..0..0..0..1

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

Cf. A282996.

cp's OEIS Frontend

A282990 Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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A282991 Number of nX3 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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A282992 Number of n X 4 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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A282993 Number of nX5 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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A282994 Number of nX6 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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A282995 Number of nX7 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

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