A199655 -id:A199655 - 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.

A200801 T(n,k) is the number of n X k 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, 2, 2, 5, 15, 5, 15, 178, 178, 15, 51, 2614, 9880, 2614, 51, 187, 40148, 583813, 583813, 40148, 187, 715, 622645, 34679839, 132636590, 34679839, 622645, 715, 2795, 9676364, 2060918000, 30147154218, 30147154218, 2060918000, 9676364, 2795

Offset: 1

R. H. Hardin, Nov 22 2011

			Table starts:
.....1...........2.................5......................15
.....2..........15...............178....................2614
.....5.........178..............9880..................583813
....15........2614............583813...............132636590
....51.......40148..........34679839.............30147154218
...187......622645........2060918000...........6852264918471
...715.....9676364......122478253815........1557479347400065
..2795...150442627.....7278777317468......354005859128023982
.11051..2339207390...432571571252989....80463441477635545163
.43947.36372631268.25707362563355693.18288865135614195620421
...
Some solutions for n=5 and k=3:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..2..0..0....0..1..1....0..0..2....2..2..0....2..2..0....2..2..0....2..1..2
..2..3..3....1..0..2....3..1..0....1..1..1....3..2..2....0..0..1....0..1..3
..2..2..0....3..2..1....3..3..0....2..2..1....3..1..3....1..1..1....1..1..2

Ron Hardin, Table of n, a(n) for n = 1..97

Main diagonal is A200794.
Columns 1..7 are A007581(n-1), A200795, A200796, A200797, A200798, A200799, A200780.
Cf. A199655, A198528.

A199649 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

2, 14, 113, 953, 8037, 67774, 571530, 4819638, 40643380, 342740340, 2890284724, 24373395288, 205537673480, 1733272476824, 14616461440144, 123258718919184, 1039424750772560, 8765333779162336, 73916920107029408, 623331776719986016

Offset: 1

R. H. Hardin, Nov 08 2011

nonn

Column 2 of A199655.

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

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

Cf. A199655.

Empirical: a(n) = 8*a(n-1) + 4*a(n-2) - 2*a(n-3) - 8*a(n-4) for n>6.

Empirical g.f.: x*(2 - 2*x - 7*x^2 - 3*x^3 + 5*x^4 + 4*x^5) / (1 - 8*x - 4*x^2 + 2*x^3 + 8*x^4). - Colin Barker, Mar 02 2018

A199650 Number of nX3 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

5, 113, 2584, 59212, 1357484, 31120632, 713445976, 16355879648, 374961537040, 8596061907680, 197066293538400, 4517780870646656, 103570953858672192, 2374383085485820032, 54433167085958461312, 1247890324488906825728

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 3 of A199655

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

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

Empirical: a(n) = 21*a(n-1) +44*a(n-2) +8*a(n-3) -96*a(n-4) -364*a(n-5) -264*a(n-6) +256*a(n-7) +288*a(n-8) +64*a(n-9) for n>10

A199651 Number of nX4 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

14, 953, 59212, 3695683, 230693158, 14399942873, 898852775335, 56106912155198, 3502225890582058, 218610965399514236, 13645822881807986686, 851780155556891684028, 53168609887984551128913, 3318815376219262701965237

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 4 of A199655

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

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

Empirical: a(n) = 60*a(n-1) +157*a(n-2) -186*a(n-3) -11412*a(n-4) -1614*a(n-5) +148235*a(n-6) -464921*a(n-7) -2730456*a(n-8) +11303105*a(n-9) +29242473*a(n-10) -103029710*a(n-11) -216889526*a(n-12) +436759588*a(n-13) +1010594719*a(n-14) -529467638*a(n-15) -1980627795*a(n-16) -809314204*a(n-17) -566374358*a(n-18) +1148311243*a(n-19) +1261859278*a(n-20) +753254801*a(n-21) -240681242*a(n-22) -120679796*a(n-23) -174398008*a(n-24) -109877696*a(n-25) -6812544*a(n-26) +7732736*a(n-27) +5814784*a(n-28) +1263616*a(n-29) +155648*a(n-30) +98304*a(n-31) for n>32

A199652 Number of nX5 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

41, 8037, 1357484, 230693158, 39209840355, 6663970316970, 1132589231853096, 192491652879392515, 32715334199617664326, 5560205218374521415185, 944996676143473092852595, 160608949278619262130353064

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 5 of A199655

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

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

A199653 Number of nX6 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

122, 67774, 31120632, 14399942873, 6663970316970, 3083761998081891, 1427019666767669979, 660357476435139192982, 305582323780950052573456, 141409100632588861437301956, 65437468685616944338442793185

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 6 of A199655

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

R. H. Hardin, Table of n, a(n) for n = 1..149

A199654 Number of nX7 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

365, 571530, 713445976, 898852775335, 1132589231853096, 1427019666767669979, 1797997097480559332224, 2265416280260844187870380, 2854348741463033805904551375, 3596383952736036093799275624989

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Column 7 of A199655

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

R. H. Hardin, Table of n, a(n) for n = 1..35

A199648 Number of n X n 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

1, 14, 2584, 3695683, 39209840355, 3083761998081891, 1797997097480559332224, 7771716024559573445914487875

Offset: 1

R. H. Hardin Nov 08 2011

nonn

Diagonal of A199655

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

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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A200801 T(n,k) is the number of n X k 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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A199649 Number of n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199650 Number of nX3 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199651 Number of nX4 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199652 Number of nX5 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199653 Number of nX6 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199654 Number of nX7 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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A199648 Number of n X n 0..2 arrays with values 0..2 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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