A232376 -id:A232376 - cp's OEIS frontend

A232370 Number of n X 2 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

2, 14, 58, 230, 934, 3794, 15354, 62266, 252346, 1022806, 4145638, 16802922, 68105158, 276041834, 1118844570, 4534868126, 18380594246, 74499685134, 301959937342, 1223895154962, 4960655920226, 20106384977054, 81494609451994

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

			Some solutions for n=7:
..2..1....0..3....3..2....3..0....3..0....2..3....3..0....1..0....3..2....3..1
..0..3....2..1....1..2....1..2....1..0....0..1....1..0....1..2....1..0....2..1
..0..3....0..1....1..0....3..2....3..2....0..3....1..2....3..2....1..2....2..3
..2..1....2..1....3..0....1..2....1..2....2..3....3..0....3..2....3..2....2..3
..3..1....2..3....2..1....0..3....0..3....0..1....3..2....1..2....3..1....0..1
..0..2....2..1....2..3....0..1....2..1....3..2....1..0....3..0....2..1....0..1
..3..2....0..1....2..3....2..3....3..1....3..2....3..0....1..2....0..3....2..3

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

Column 2 of A232376.

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

Empirical g.f.: 2*x*(1 + 5*x + 8*x^2 + 2*x^3 - 6*x^4 + x^5 + x^6) / ((1 + x)*(1 - 3*x - 4*x^2 - 2*x^3 + 4*x^4 - x^5 - x^6)). - Colin Barker, Oct 05 2018

A232371 Number of nX3 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

4, 74, 586, 4550, 36574, 292122, 2324142, 18574882, 148225606, 1182879814, 9441116934, 75346596778, 601334070966, 4799220047514, 38302112010658, 305686073938078, 2439655331781498, 19470682813562030, 155393901867403394

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Column 3 of A232376

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

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

Empirical: a(n) = 4*a(n-1) +17*a(n-2) +74*a(n-3) +170*a(n-4) +1012*a(n-5) +2868*a(n-6) +3592*a(n-7) +4816*a(n-8) +5356*a(n-9) +6245*a(n-10) +4504*a(n-11) +2633*a(n-12) +954*a(n-13) +756*a(n-14) +216*a(n-15)

A232372 Number of nX4 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

8, 296, 4404, 63744, 957232, 14297980, 213082596, 3180405572, 47457708756, 708101568772, 10565916295512, 157657615301852, 2352456485793908, 35101771262909316, 523764821849080236, 7815262731268162904

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Column 4 of A232376

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

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

Empirical: a(n) = 10*a(n-1) +46*a(n-2) +374*a(n-3) +330*a(n-4) +2418*a(n-5) +7211*a(n-6) +9104*a(n-7) +1944*a(n-8) -21557*a(n-9) -54205*a(n-10) -77028*a(n-11) -83393*a(n-12) -57615*a(n-13) -34140*a(n-14) -9235*a(n-15) -944*a(n-16) +2734*a(n-17) +385*a(n-18) +30*a(n-19) -35*a(n-20) +138*a(n-21) -4*a(n-22)

A232373 Number of nX5 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

14, 1130, 32722, 927706, 27133338, 789866870, 22946925502, 667514680522, 19413840326186, 564595278464614, 16420169035941450, 477546295651389890, 13888417395173915122, 403915461426343969950, 11747031027223155160682

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Column 5 of A232376

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Empirical recurrence of order 64 (see link above)

A232374 Number of nX6 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

26, 4682, 259458, 14326374, 825606450, 47301712998, 2706080691402, 154987416800398, 8875595994390694, 508249649361525870, 29105003808620979142, 1666700158869294743494, 95443569491003523718078

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Column 6 of A232376

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

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

A232375 Number of nX7 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

48, 19448, 2046700, 219597458, 24945468636, 2824295623804, 319646954776850, 36234058732024820, 4107330198377776652, 465585399247158982768, 52778440824390526548132, 5982947009339446194736266

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Column 7 of A232376

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

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

A232377 Number of 2Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

1, 14, 74, 296, 1130, 4682, 19448, 79592, 326810, 1343042, 5516132, 22658744, 93073958, 382310690, 1570402928, 6450645104, 26496901994, 108839752922, 447074397188, 1836420218672, 7543351642070, 30985365821066, 127276699845344, 522806747988728, 2147501432084138

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Row 2 of A232376.

			Some solutions for n=7
..3..0..1..2..1..0..3....0..3..2..3..0..3..0....2..1..2..3..0..3..2
..3..2..3..0..1..0..3....2..1..0..3..2..1..0....2..3..2..3..0..1..2

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

Empirical: a(n) = 3*a(n-1) +a(n-2) +13*a(n-3) +26*a(n-5) -4*a(n-6) +24*a(n-7) +16*a(n-8) for n>9.

Empirical g.f.: x + 2*x^2*(-7 -16*x -30*x^2 +7*x^3 -17*x^4 -30*x^5 -4*x^6 +8*x^7) / ( (2*x^2+1)*(8*x^6 +12*x^5 -6*x^4 +7*x^3 +3*x^2 +3*x-1) ). - R. J. Mathar, Nov 27 2013

A232378 Number of 3Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

1, 58, 586, 4404, 32722, 259458, 2046700, 16005328, 125458506, 984034642, 7715900888, 60499523096, 474378832026, 3719632557790, 29165838646828, 228690711059796, 1793174932294258, 14060373065557530, 110248073913792604

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Row 3 of A232376

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

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

Empirical: a(n) = 6*a(n-1) +4*a(n-2) +69*a(n-3) +48*a(n-4) +355*a(n-5) +241*a(n-6) +1332*a(n-7) +2318*a(n-8) +448*a(n-9) -1416*a(n-10) -784*a(n-11) +64*a(n-12) +48*a(n-13) for n>14

A232379 Number of 4Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

1, 230, 4550, 63744, 927706, 14326374, 219597458, 3342549408, 50948669958, 777136688838, 11852126079904, 180743308881776, 2756349347909628, 42034903671321438, 641040165008121734, 9775973027252581380

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Row 4 of A232376

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 60

Empirical recurrence of order 60 (see link above)

A232380 Number of 5Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Original entry on oeis.org

1, 934, 36574, 957232, 27133338, 825606450, 24945468636, 747913169216, 22460676406974, 675143834470462, 20291549259837168, 609804313253059260, 18326215546732616794, 550758040677362295570, 16551923665278410826856

Offset: 1

R. H. Hardin, Nov 23 2013

nonn

Row 5 of A232376

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

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

cp's OEIS Frontend

A232370 Number of n X 2 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A232371 Number of nX3 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232372 Number of nX4 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232373 Number of nX5 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232374 Number of nX6 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

A232375 Number of nX7 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

A232377 Number of 2Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232378 Number of 3Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232379 Number of 4Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A232380 Number of 5Xn 0..3 arrays with every 0 next to a 1, every 1 next to a 2 and every 2 next to a 3 horizontally, diagonally or antidiagonally, and no adjacent values equal.

Views

Author

Keywords

Comments

Examples

Links