A200801 -id:A200801 - cp's OEIS frontend

A198528 T(n,k) is the number of n X k 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

1, 2, 2, 5, 15, 5, 15, 193, 193, 15, 52, 3660, 16714, 3660, 52, 202, 81844, 1877316, 1877316, 81844, 202, 855, 1948672, 222590953, 1084539825, 222590953, 1948672, 855, 3845, 47436498, 26670041125, 634586561196, 634586561196, 26670041125

Offset: 1

R. H. Hardin, Oct 26 2011

			Table starts:
.....1............2...................5......................15
.....2...........15.................193....................3660
.....5..........193...............16714.................1877316
....15.........3660.............1877316..............1084539825
....52........81844...........222590953............634586561196
...202......1948672.........26670041125.........371815743708461
...855.....47436498.......3201911378187......217885196778717007
..3845...1163606279.....384557171168810...127683385189755792564
.18002..28617909415...46189600128813487.74824145653256981522691
.86472.704465305625.5547962760669962158
Some solutions for n=6 and k=4:
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..2..2..1..2....2..2..1..2....2..2..1..2....2..2..1..2....2..2..1..2
..2..2..3..2....0..3..1..2....3..0..0..3....2..0..1..0....0..3..4..4
..1..4..0..4....3..2..4..4....3..1..4..3....1..3..0..0....3..3..0..4

R. H. Hardin, Table of n, a(n) for n = 1..84

Main diagonal is A198521.
Columns 1..7 are A056272, A198522, A198523, A198524, A198525, A198526, A198527.
Cf. A199655, A200801.

A200795 Number of n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

2, 15, 178, 2614, 40148, 622645, 9676364, 150442627, 2339207390, 36372631268, 565564863676, 8794081340271, 136740955582530, 2126212947243743, 33060918081784912, 514070948321926226, 7993393871925768124

Offset: 1

R. H. Hardin, Nov 22 2011

nonn

Column 2 of A200801.

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

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

Cf. A200801.

Empirical: a(n) = 18*a(n-1) - 35*a(n-2) - 48*a(n-3) - 11*a(n-4) + 90*a(n-5) + 36*a(n-6) - 12*a(n-7) - 36*a(n-8) for n>10.

Empirical g.f.: x*(1 - x)*(2 - 19*x - 41*x^2 - 10*x^3 + 58*x^4 + 58*x^5 - 28*x^7 - 12*x^8) / ((1 - 3*x - x^2 + 2*x^4)*(1 - 15*x - 9*x^2 + 6*x^3 + 18*x^4)). - Colin Barker, Mar 02 2018

A200796 Number of nX3 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

5, 178, 9880, 583813, 34679839, 2060918000, 122478253815, 7278777317468, 432571571252989, 25707362563355693, 1527766813187552208, 90793889493222901029, 5395804057415427972197, 320668071260622898796015

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 3 of A200801

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

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

Empirical: a(n) = 60*a(n-1) -17*a(n-2) -964*a(n-3) -2509*a(n-4) +968*a(n-5) +23125*a(n-6) +31652*a(n-7) -4566*a(n-8) -17118*a(n-9) -29646*a(n-10) -74826*a(n-11) -64125*a(n-12) -13932*a(n-13) +4131*a(n-14) +1458*a(n-15) for n>16

A200797 Number of nX4 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

15, 2614, 583813, 132636590, 30147154218, 6852264918471, 1557479347400065, 354005859128023982, 80463441477635545163, 18288865135614195620421, 4156951055108642793860100, 944850429287655687332694651

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 4 of A200801

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

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

Empirical: a(n) = 226*a(n-1) +397*a(n-2) -21234*a(n-3) -497498*a(n-4) +2087766*a(n-5) +34773209*a(n-6) -15109862*a(n-7) -1344245435*a(n-8) +6305961810*a(n-9) -9646383486*a(n-10) -311210406120*a(n-11) +818951464312*a(n-12) +7068765097660*a(n-13) -15075608645540*a(n-14) -89765346075158*a(n-15) +83122511102408*a(n-16) +562758507641100*a(n-17) +211301619877576*a(n-18) -1363882902513610*a(n-19) -3093844768642228*a(n-20) +3909385497592574*a(n-21) +12063883361116060*a(n-22) -8119400268962692*a(n-23) -27724078036879543*a(n-24) -2195647624835104*a(n-25) +17503376946283795*a(n-26) +13937597848821644*a(n-27) +21063587960493070*a(n-28) +19559907770565622*a(n-29) -10692765489736685*a(n-30) -24922540031602668*a(n-31) -4863390875436761*a(n-32) -21563816326872032*a(n-33) -31429218919732322*a(n-34) -6405644638575092*a(n-35) +28158640181918660*a(n-36) +26831253270589974*a(n-37) +12473963843739616*a(n-38) +1775794465292012*a(n-39) -5284490896805036*a(n-40) -6920386914042164*a(n-41) -4547920088065892*a(n-42) -1201731389529908*a(n-43) +263989556748732*a(n-44) +650291914832328*a(n-45) +365189349172464*a(n-46) +98577715906512*a(n-47) -3548230253856*a(n-48) -15222363587136*a(n-49) -7040558081664*a(n-50) -2182723137792*a(n-51) -417125915136*a(n-52) -58773123072*a(n-53) for n>54

A200798 Number of nX5 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

51, 40148, 34679839, 30147154218, 26207146328784, 22781978610167987, 19804473216531794553, 17216114684815070366422, 14966043352402318383229010, 13010046560219625329665338289, 11309690043874236949034566968117

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 5 of A200801

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

R. H. Hardin, Table of n, a(n) for n = 1..155

A200799 Number of n X 6 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

187, 622645, 2060918000, 6852264918471, 22781978610167987, 75743730886453371522, 251826890612151285556718, 837254535307721417534184492, 2783639010978210077196779661724

Offset: 1

R. H. Hardin, Nov 22 2011

nonn

Column 6 of A200801.

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

R. H. Hardin, Table of n, a(n) for n = 1..28

Cf. A200801.

A200794 Number of n X n 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

1, 15, 9880, 132636590, 26207146328784, 75743730886453371522, 3202145671418507455058837791

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Diagonal of A200801

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

A200800 Number of nX7 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

715, 9676364, 122478253815, 1557479347400065, 19804473216531794553, 251826890612151285556718, 3202145671418507455058837791

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 7 of A200801

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

cp's OEIS Frontend

A198528 T(n,k) is the number of n X k 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200795 Number of n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200796 Number of nX3 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200797 Number of nX4 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200798 Number of nX5 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200799 Number of n X 6 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200794 Number of n X n 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A200800 Number of nX7 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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