A218842 -id:A218842 - cp's OEIS frontend

A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.

1, 2, 7, 21, 65, 200, 616, 1897, 5842, 17991, 55405, 170625, 525456, 1618192, 4983377, 15346786, 47261895, 145547525, 448227521, 1380359512, 4250949112, 13091204281, 40315615410, 124155792775, 382349636061, 1177482265857, 3626169232672, 11167134898976

Offset: 0

R. H. Hardin, Nov 07 2012

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

R. H. Hardin, Table of n, a(n) for n = 0..210
Index entries for linear recurrences with constant coefficients, signature (2,3,1).

Column 2 of A218842.

a:= n-> (<<0|1|0>, <0|0|1>, <1|3|2>>^n. <<1, 2, 7>>)[1$2]:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 21 2020

LinearRecurrence[{2, 3, 1}, {1, 2, 7}, 30] (* Paolo Xausa, Jan 29 2025 *)

a(n) = 2*a(n-1) +3*a(n-2) +a(n-3).
G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1- x*(4*k+2 +3*x+x^2)/(x*(4*k+4 +3*x+x^2) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013
G.f.: 1/(1-2*x-3*x^2-x^3). - Alois P. Heinz, Apr 21 2020

a(0)=1 prepended and first g.f. adapted by Alois P. Heinz, Apr 21 2020

A218837 Unmatched value maps: number of n X 3 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 3 array.

Original entry on oeis.org

4, 20, 93, 436, 2043, 9573, 44857, 210190, 984904, 4615043, 21625074, 101330329, 474811581, 2224862385, 10425214612, 48850257184, 228901534957, 1072582125992, 5025883366023, 23550181377025, 110350957732161, 517080258425742

Offset: 1

R. H. Hardin, Nov 07 2012

nonn

Column 3 of A218842.

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

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

Cf. A218842.

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

Empirical g.f.: x*(2 + x)^2 / (1 - 4*x - 3*x^2 - x^3). - Colin Barker, Mar 10 2018

A218838 Unmatched value maps: number of n X 4 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 4 array.

Original entry on oeis.org

7, 57, 453, 3617, 28888, 230726, 1842766, 14717828, 117548611, 938839259, 7498337380, 59887849061, 478313295496, 3820200795065, 30511244937310, 243687732023270, 1946289338913085, 15544656923507264, 124152331330394548

Offset: 1

R. H. Hardin, Nov 07 2012

nonn

Column 4 of A218842.

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

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

Cf. A218842.

Empirical: a(n) = 7*a(n-1) + 5*a(n-2) + 24*a(n-3) - 9*a(n-4) + 9*a(n-5) for n>6.

Empirical g.f.: x*(7 + 8*x + 19*x^2 - 7*x^3 - x^4 + 3*x^5) / (1 - 7*x - 5*x^2 - 24*x^3 + 9*x^4 - 9*x^5). - Colin Barker, Mar 10 2018

A218839 Unmatched value maps: number of nX5 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX5 array.

Original entry on oeis.org

12, 156, 2050, 26635, 346501, 4507281, 58634265, 762745363, 9922198586, 129073371922, 1679056577224, 21842080049186, 284133645307551, 3696164842194424, 48081720559244098, 625473146037672596

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Column 5 of A218842

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

R. H. Hardin, Table of n, a(n) for n = 1..65

Empirical: a(n) = 12*a(n-1) +6*a(n-2) +103*a(n-3) -128*a(n-4) -41*a(n-5) -630*a(n-6) -523*a(n-7) +1154*a(n-8) -93*a(n-9) +762*a(n-10) -787*a(n-11) -416*a(n-12) +549*a(n-13) -178*a(n-14) +35*a(n-15) +11*a(n-16) -7*a(n-17) for n>18

A218840 Unmatched value maps: number of nX6 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX6 array.

Original entry on oeis.org

21, 438, 9516, 201960, 4299802, 91513161, 1948262831, 41475009100, 882920599454, 18795714385533, 400125250527550, 8517908622924528, 181330147341356981, 3860175542316616321, 82175828913427711206, 1749367816354069818496

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Column 6 of A218842

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

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

A218841 Unmatched value maps: number of nX7 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX7 array.

Original entry on oeis.org

37, 1220, 44129, 1530846, 53372068, 1858438456, 64756459689, 2256078606791, 78598915311375, 2738314667345978, 95400355881324823, 3323658089304061344, 115793113908855836331, 4034122981125875986810, 140545041981707228122666

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Column 7 of A218842

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

R. H. Hardin, Table of n, a(n) for n = 1..20

A218843 Unmatched value maps: number of 2 X n binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 2 X n array.

Original entry on oeis.org

1, 7, 20, 57, 156, 438, 1220, 3398, 9468, 26380, 73496, 204780, 570556, 1589672, 4429140, 12340436, 34382820, 95797176, 266909376, 743660900, 2071982512, 5772942284, 16084528900, 44814595084, 124862092120, 347889834096

Offset: 1

R. H. Hardin, Nov 07 2012

nonn

Row 2 of A218842.

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

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

Cf. A218842.

Empirical: a(n) = 2*a(n-1) + a(n-2) + 3*a(n-3) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>9.

Empirical g.f.: x*(1 + 5*x + 5*x^2 + 7*x^3 + x^4 + 7*x^5 + x^6 - 2*x^8) / (1 - 2*x - x^2 - 3*x^3 - 2*x^5 - 2*x^6 + 2*x^7). - Colin Barker, Jul 24 2018

A218844 Unmatched value maps: number of 3Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 3Xn array.

Original entry on oeis.org

1, 21, 93, 453, 2050, 9516, 44129, 204780, 950346, 4410194, 20465923, 94974721, 440743516, 2045330613, 9491634200, 44047218242, 204407115009, 948579057090, 4402010267626, 20428127976053, 94799509246526, 439930030199648

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Row 3 of A218842

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

R. H. Hardin, Table of n, a(n) for n = 1..53

A218845 Unmatched value maps: number of 4Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 4Xn array.

Original entry on oeis.org

1, 65, 436, 3617, 26635, 201960, 1530846, 11617859, 88207678, 669575111, 5082650645, 38581655789, 292872656082, 2223190550341, 16876170296292, 128106451991984, 972451948238336, 7381852115978817, 56035406540101182

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Row 4 of A218842

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

R. H. Hardin, Table of n, a(n) for n = 1..37

A218846 Unmatched value maps: number of 5Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 5Xn array.

Original entry on oeis.org

1, 200, 2043, 28888, 346501, 4299802, 53372068, 663615890, 8258480840, 102739744908, 1278038244556, 15897575084961, 197757402894222, 2460009603174968, 30601283457873781, 380663991433804098

Offset: 1

R. H. Hardin Nov 07 2012

nonn

Row 5 of A218842

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

R. H. Hardin, Table of n, a(n) for n = 1..42

cp's OEIS Frontend

A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.

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A218837 Unmatched value maps: number of n X 3 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 3 array.

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A218838 Unmatched value maps: number of n X 4 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 4 array.

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A218839 Unmatched value maps: number of nX5 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX5 array.

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A218840 Unmatched value maps: number of nX6 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX6 array.

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A218841 Unmatched value maps: number of nX7 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX7 array.

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A218843 Unmatched value maps: number of 2 X n binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 2 X n array.

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A218844 Unmatched value maps: number of 3Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 3Xn array.

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A218845 Unmatched value maps: number of 4Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 4Xn array.

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A218846 Unmatched value maps: number of 5Xn binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 5Xn array.

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