A233082 -id:A233082 - cp's OEIS frontend

A233076 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

1, 14, 1985, 1588262, 6938214854, 165407945648306, 21520525142517911969, 15280137439726087042287674, 59207172638901578439239726940974, 1251961921151721201415260511387809535370

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Diagonal of A233082.

			Some solutions for n=3
..0..0..0....0..1..1....0..1..3....0..0..0....0..1..3....0..1..1....0..0..1
..1..0..0....1..3..1....3..2..0....0..0..1....1..3..2....1..1..0....0..0..0
..0..0..2....2..3..1....3..2..2....1..1..0....2..3..3....0..2..2....0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..13

Cf. A233082.

A233077 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

5, 95, 1985, 41675, 875165, 18378455, 385947545, 8104898435, 170202867125, 3574260209615, 75059464401905, 1576248752439995, 33101223801239885, 695125699826037575, 14597639696346789065, 306550433623282570355

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=4:
..0..1..3....0..1..0....0..1..1....0..0..1....0..0..0....0..1..1....0..0..0
..3..1..3....1..0..0....0..0..1....1..1..3....0..0..1....0..0..2....1..0..0
..0..1..3....0..2..3....2..0..1....0..1..0....2..3..3....2..3..1....0..1..1
..1..1..0....0..2..0....2..0..2....0..0..2....1..3..1....1..0..1....1..1..0

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

Column 3 of A233082.

Empirical: a(n) = 22*a(n-1) - 21*a(n-2).
Conjectures from Colin Barker, Oct 07 2018: (Start)
G.f.: 5*x*(1 - 3*x) / ((1 - x)*(1 - 21*x)).
a(n) = (7 + 3^(1+n)*7^n) / 14.
(End)

A233078 Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

14, 662, 32414, 1588262, 77824814, 3813415862, 186857377214, 9156011483462, 448644562689614, 21983583571791062, 1077195595017762014, 52782584155870338662, 2586346623637646594414, 126730984558244683126262

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=3:
..0..0..1..3....0..1..1..3....0..0..0..0....0..0..1..1....0..1..1..0
..2..3..1..1....3..1..1..3....0..1..0..0....1..3..3..1....3..1..1..0
..1..0..1..3....1..3..1..1....0..1..1..3....1..3..3..1....3..1..0..2

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

Column 4 of A233082.

Empirical: a(n) = 50*a(n-1) - 49*a(n-2).
Conjectures from Colin Barker, Oct 07 2018: (Start)
G.f.: 2*x*(7 - 19*x) / ((1 - x)*(1 - 49*x)).
a(n) = (49 + 27*49^n) / 98.
(End)

A233079 Number of n X 5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

41, 4631, 529862, 60632429, 6938214854, 793945203881, 90851753687090, 10396235291448605, 1189649113515482414, 136132453105625552657, 15577740173984637831242, 1782572659143148713774245

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=2:
..0..0..1..3..3....0..0..1..0..0....0..0..1..0..0....0..0..0..0..1
..0..1..3..3..1....2..3..2..0..0....1..1..1..1..1....0..1..1..1..0

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

Column 5 of A233082.

Empirical: a(n) = 118*a(n-1) - 411*a(n-2) + 294*a(n-3).

Empirical g.f.: x*(41 - 207*x + 255*x^2) / ((1 - x)*(1 - 117*x + 294*x^2)). - Colin Barker, Oct 07 2018

A233080 Number of n X 6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

122, 32414, 8662343, 2315298290, 618844579511, 165407945648306, 44211082661517335, 11816964557611382642, 3158498796072853930295, 844219731401266443119474, 225647372661155279429241623

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=2:
..0..1..0..0..2..0....0..0..1..1..3..3....0..1..3..2..2..2....0..1..0..2..0..1
..1..1..0..0..2..2....1..1..0..1..1..0....0..1..0..2..0..1....0..2..2..2..0..2

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

Column 6 of A233082.

Empirical: a(n) = 283*a(n-1) - 4251*a(n-2) + 13573*a(n-3) - 9604*a(n-4).

Empirical g.f.: x*(122 - 2112*x + 7803*x^2 - 8771*x^3) / ((1 - x)*(1 - 282*x + 3969*x^2 - 9604*x^3)). - Colin Barker, Oct 07 2018

A233081 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

365, 226895, 141615905, 88417171553, 55204524946337, 34467813715307081, 21520525142517911969, 13436680693956706599305, 8389404393896088886849313, 5238057500238107310826087913, 3270464157841452851203199640929

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Column 7 of A233082

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

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

Empirical: a(n) = 693*a(n-1) -44261*a(n-2) +890611*a(n-3) -7150206*a(n-4) +22034516*a(n-5) -15731352*a(n-6)

A233083 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

3, 14, 95, 662, 4631, 32414, 226895, 1588262, 11117831, 77824814, 544773695, 3813415862, 26693911031, 186857377214, 1308001640495, 9156011483462, 64092080384231, 448644562689614, 3140511938827295, 21983583571791062

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=5:
..0..1..1..3..2....0..0..1..0..2....0..1..1..3..3....0..1..0..2..0
..1..3..2..2..3....2..0..1..0..0....1..1..3..3..3....0..1..0..0..0

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

Row 2 of A233082.

Empirical: a(n) = 8*a(n-1) - 7*a(n-2) for n>3.
Conjectures from Colin Barker, Oct 07 2018: (Start)
G.f.: x*(3 - 10*x + 4*x^2) / ((1 - x)*(1 - 7*x)).
a(n) = (49 + 27*7^n) / 98 for n>1.
(End)

A233084 Number of 3 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

10, 122, 1985, 32414, 529862, 8662343, 141615905, 2315203034, 37850025182, 618789971363, 10116268804625, 165385509256454, 2703799908891302, 44202989610119183, 722651215442080145, 11814241158484224674

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

			Some solutions for n=4:
..0..1..0..2....0..1..1..3....0..1..3..1....0..1..3..2....0..1..0..2
..1..0..0..0....1..1..3..3....0..1..3..3....1..3..2..3....0..0..0..0
..1..0..0..2....1..3..3..2....3..3..1..1....3..3..3..2....1..0..1..0

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

Row 3 of A233082.

Empirical: a(n) = 19*a(n-1) - 45*a(n-2) + 27*a(n-3) for n>5.

Empirical g.f.: x*(10 - 68*x + 117*x^2 - 81*x^3 + 27*x^4) / ((1 - x)*(1 - 18*x + 27*x^2)). - Colin Barker, Oct 07 2018

A233085 Number of 4Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

36, 1094, 41675, 1588262, 60632429, 2315298290, 88417171553, 3376534087742, 128945571641429, 4924269835697930, 188051703434648393, 7181459293743807062, 274250946368131595069, 10473300553139406347810, 399962246005236076609073

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Row 4 of A233082

			Some solutions for n=3
..0..1..0....0..0..0....0..1..1....0..0..0....0..1..0....0..1..1....0..1..0
..0..0..2....0..0..1....1..0..1....0..1..0....3..2..3....1..1..1....3..1..3
..0..2..2....2..0..0....1..3..3....0..2..0....2..2..2....1..0..1....3..1..0
..3..3..2....0..1..0....3..1..3....0..1..1....2..0..2....1..0..0....3..2..0

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

Empirical: a(n) = 49*a(n-1) -450*a(n-2) +1466*a(n-3) -1853*a(n-4) +789*a(n-5) for n>8

A233086 Number of 5Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

Original entry on oeis.org

136, 9842, 875165, 77824814, 6938214854, 618844579511, 55204524946337, 4924730456325950, 439332915121147814, 39192753113196729071, 3496374576586734284957, 311910622275336283545350

Offset: 1

R. H. Hardin, Dec 03 2013

nonn

Row 5 of A233082

			Some solutions for n=2
..0..0....0..1....0..0....0..0....0..1....0..1....0..1....0..1....0..0....0..1
..1..1....3..2....1..3....1..3....3..3....1..1....3..1....3..2....1..0....1..1
..0..1....3..1....2..0....3..3....3..1....0..0....1..0....2..2....1..0....3..2
..0..1....1..3....2..2....3..3....0..1....0..0....0..0....0..1....1..1....2..2
..3..2....2..0....0..2....3..2....3..2....0..1....0..2....3..1....1..0....3..2

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

Empirical: a(n) = 132*a(n-1) -4507*a(n-2) +66832*a(n-3) -492772*a(n-4) +1765654*a(n-5) -2023881*a(n-6) -4686284*a(n-7) +16006509*a(n-8) -16068834*a(n-9) +5437152*a(n-10) for n>14

cp's OEIS Frontend

A233076 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233077 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233078 Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233079 Number of n X 5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233080 Number of n X 6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233081 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233083 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233084 Number of 3 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233085 Number of 4Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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A233086 Number of 5Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

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