A185540 -id:A185540 - cp's OEIS frontend

A185535 1/6 the number of n X 2 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

1, 11, 110, 1155, 12105, 127190, 1336205, 14039455, 147510990, 1549891055, 16284627805, 171101820790, 1797758782905, 18888967243155, 198465493076590, 2085267630701755, 21909809227375505, 230205338311698390

Offset: 1

R. H. Hardin, Jan 30 2011

nonn

Column 2 of A185540.

			Some solutions for 3 X 2 with a(1,1)=0:
..0..4....0..0....0..0....0..0....0..0....0..0....0..3....0..5....0..0....0..5
..0..4....5..1....0..5....1..1....1..3....0..2....0..3....0..5....2..0....0..5
..0..4....5..1....0..5....3..3....1..3....2..2....3..3....3..3....2..0....5..5

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A185540.

Empirical: a(n) = 9*a(n-1) + 19*a(n-2) - 25*a(n-3) - 75*a(n-4) - 125*a(n-5).

Empirical g.f.: x*(1 + 2*x - 8*x^2 - 19*x^3 - 30*x^4) / (1 - 9*x - 19*x^2 + 25*x^3 + 75*x^4 + 125*x^5). - Colin Barker, Apr 16 2018

A185536 1/6 the number of nX3 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

1, 110, 2990, 127570, 4403225, 167398110, 6079401960, 225574291125, 8285469213945, 305786452982260, 11260066599241195, 415073544779136460, 15292958690004125565, 563586551260018728505, 20767361004817999220125

Offset: 1

R. H. Hardin Jan 30 2011

nonn

Column 3 of A185540

			Some solutions for 5X3 with a(1,1)=0
..0..0..0....0..0..0....0..0..3....0..0..3....0..0..0....0..0..0....0..3..3
..0..3..3....0..3..3....0..0..3....0..3..3....0..3..3....0..3..3....0..0..0
..4..0..0....4..1..3....3..3..1....1..0..0....0..2..2....2..2..3....5..2..0
..4..4..4....4..1..0....5..5..1....1..1..2....3..4..2....2..4..0....5..2..2
..5..5..4....0..0..0....4..4..4....5..5..2....3..4..4....2..4..0....5..5..5

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=22*a(n-1)+638*a(n-2)-2567*a(n-3)-29583*a(n-4)+27088*a(n-5)+209637*a(n-6)+620796*a(n-7)-1634411*a(n-8)-4083145*a(n-9)+17086070*a(n-10)-21827225*a(n-11)-42404829*a(n-12)-73933685*a(n-13)+687497360*a(n-14)-669370750*a(n-15)-1844490625*a(n-16)+8145764375*a(n-17)+6297734375*a(n-18)-14443984375*a(n-19)-34831953125*a(n-20)-42570312500*a(n-21)-47656250000*a(n-22)-78125000000*a(n-23)

A185537 1/6 the number of nX4 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

6, 1155, 127570, 17526450, 2241330570, 295044602325, 38418831900875, 5024252800116630, 655951718326130130, 85695581922306489845, 11192649881286988768850, 1462013677990229903804335

Offset: 1

R. H. Hardin Jan 30 2011

nonn

Column 4 of A185540

			Some solutions for 3X4 with a(1,1)=0
..0..5..5..4....0..2..5..5....0..0..2..4....0..1..2..2....0..0..0..2
..0..1..5..4....0..2..3..5....1..3..2..4....0..1..0..4....3..2..2..2
..1..1..3..3....2..2..3..3....1..3..4..4....5..5..0..4....3..5..5..5

R. H. Hardin, Table of n, a(n) for n = 1..48

A185538 1/6 the number of nX5 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

11, 12105, 4403225, 2241330570, 994633804270, 468362874353295

Offset: 1

R. H. Hardin Jan 30 2011

nonn

Column 5 of A185540

			Some solutions for 3X5 with a(1,1)=0
..0..0..0..4..4....0..0..3..3..5....0..0..0..3..4....0..0..0..0..1
..0..3..3..2..4....3..3..4..3..5....0..3..1..3..4....0..3..2..1..1
..0..0..0..2..2....0..0..4..4..5....0..3..1..5..5....0..3..2..5..5

A185539 1/6 the number of nX6 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

41, 127190, 167398110, 295044602325, 468362874353295

Offset: 1

R. H. Hardin Jan 30 2011

nonn

Column 6 of A185540

			Some solutions for 3X6 with a(1,1)=0
..0..0..3..4..2..2....0..0..2..2..2..4....0..0..3..1..0..0....0..0..3..5..3..3
..0..3..3..4..4..2....0..3..3..1..2..4....0..3..3..1..3..4....0..3..3..5..2..3
..0..0..0..2..2..2....0..0..0..1..2..2....0..0..0..3..3..4....0..0..0..5..2..2

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A185535 1/6 the number of n X 2 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A185536 1/6 the number of nX3 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A185537 1/6 the number of nX4 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A185538 1/6 the number of nX5 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A185539 1/6 the number of nX6 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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