A218354 -id:A218354 - cp's OEIS frontend

A218348 Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX2 array.

3, 11, 41, 149, 547, 2007, 7361, 27001, 99043, 363299, 1332617, 4888173, 17930307, 65770159, 241251521, 884934705, 3246028995, 11906758971, 43675182633, 160204937605, 587647732323, 2155550649479, 7906775346689, 29002842683433

Offset: 1

R. H. Hardin, Oct 26 2012

Number of dominating sets in the ladder graph P_2 X P_n. - Andrew Howroyd, May 10 2017

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Eric Weisstein's World of Mathematics, Dominating Set
Eric Weisstein's World of Mathematics, Ladder Graph
Index entries for linear recurrences with constant coefficients, signature (3,2,2,-1,-1).

Column 2 of A218354.

Cf. A284663, A284702.

LinearRecurrence[{3, 2, 2, -1, -1}, {3, 11, 41, 149, 547}, 20]  (* Eric W. Weisstein, Jun 14 2017 *)
CoefficientList[Series[(x (3 + 2 x + 2 x^2 - 2 x^3 - x^4))/(1 - 3 x - 2 x^2 - 2 x^3 + x^4 + x^5), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 14 2017 *)
Table[RootSum[1 + # - 2 #^2 - 2 #^3 - 3 #^4 + #^5 &, (-167 + 525 # - 73 #^2 + 819 #^3 - 218 #^4) #^n &]/2102, {n, 20}] (* Eric W. Weisstein, Jul 13 2017 *)

Vec((3+2*x+2*x^2-2*x^3-x^4)/(1-3*x-2*x^2-2*x^3+x^4+x^5)+O(x^50)) \\ Andrew Howroyd, May 10 2017

a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).

G.f.: x*(3 + 2*x + 2*x^2 - 2*x^3 - x^4)/(1 - 3*x - 2*x^2 - 2*x^3 + x^4 + x^5). - Andrew Howroyd, May 10 2017

A218349 Hilltop maps: number of nX3 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX3 array.

Original entry on oeis.org

5, 41, 291, 2069, 14811, 105913, 757305, 5415209, 38722037, 276885777, 1979899795, 14157473937, 101234450215, 723887182917, 5176228570197, 37013146305509, 264666248964889, 1892522801570497, 13532675845407459, 96766768350125913

Offset: 1

R. H. Hardin Oct 26 2012

nonn

Column 3 of A218354

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

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

Empirical: a(n) = 6*a(n-1) +5*a(n-2) +22*a(n-3) +7*a(n-4) +8*a(n-5) -18*a(n-6) -20*a(n-7) -a(n-8) +4*a(n-9) +3*a(n-10) +a(n-12)

A218350 Hilltop maps: number of nX4 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX4 array.

Original entry on oeis.org

9, 149, 2069, 28661, 401253, 5609569, 78394141, 1095695529, 15314367301, 214044940145, 2991651891557, 41813576818545, 584417958076589, 8168264238929833, 114165795446827469, 1595666897305379897

Offset: 1

R. H. Hardin Oct 26 2012

nonn

Column 4 of A218354

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

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

Empirical: a(n) = 10*a(n-1) +36*a(n-2) +242*a(n-3) +413*a(n-4) +482*a(n-5) -720*a(n-6) -2212*a(n-7) -683*a(n-8) +466*a(n-9) +121*a(n-10) -414*a(n-11) -119*a(n-12) -100*a(n-13) +241*a(n-14) +36*a(n-15) +164*a(n-16) -44*a(n-17) +35*a(n-18) -4*a(n-19) +2*a(n-20) +2*a(n-21) -a(n-22)

A218351 Hilltop maps: number of nX5 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX5 array.

Original entry on oeis.org

17, 547, 14811, 401253, 10982565, 300126903, 8199377227, 224032447213, 6121258910011, 167250519310183, 4569773233045519, 124859601874166153, 3411530022687206815, 93212992000176142919, 2546851962811003392065

Offset: 1

R. H. Hardin Oct 26 2012

nonn

Column 5 of A218354

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

R. H. Hardin, Table of n, a(n) for n = 1..51

A218352 Hilltop maps: number of nX6 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX6 array.

Original entry on oeis.org

31, 2007, 105913, 5609569, 300126903, 16031828359, 856149291505, 45726317510017, 2442206384575879, 130435504723928475, 6966420606934069925, 372069142324752766777, 19871816932607721069123, 1061332595121563636599299

Offset: 1

R. H. Hardin Oct 26 2012

nonn

Column 6 of A218354

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

R. H. Hardin, Table of n, a(n) for n = 1..72

A218353 Hilltop maps: number of nX7 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX7 array.

Original entry on oeis.org

57, 7361, 757305, 78394141, 8199377227, 856149291505, 89373230342147, 9330728065217697, 974144457139164177, 101701766819321353361, 10617786795585969799967, 1108509971334366966147185

Offset: 1

R. H. Hardin Oct 26 2012

nonn

Column 7 of A218354

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

R. H. Hardin, Table of n, a(n) for n = 1..34

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A218348 Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX2 array.

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A218349 Hilltop maps: number of nX3 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX3 array.

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A218350 Hilltop maps: number of nX4 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX4 array.

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A218351 Hilltop maps: number of nX5 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX5 array.

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A218352 Hilltop maps: number of nX6 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX6 array.

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A218353 Hilltop maps: number of nX7 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX7 array.

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