A208175 -id:A208175 - cp's OEIS frontend

A208169 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

1, 13, 8469, 99752346, 16567902881244, 38625516979536823947, 1263976383376771173195964686, 580579239138791881884932674640711196, 3743190521310525744113304412007474906812935048

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Diagonal of A208175

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

R. H. Hardin, Table of n, a(n) for n = 1..10

A208170 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

5, 159, 8469, 473928, 26625693, 1496307201, 84091222866, 4725865313907, 265590215430897, 14925978329967384, 838829205068709369, 47141595663874099773, 2649323638611897879018, 148890075596000256587991

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 3 of A208175.

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

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

Cf. A208175.

Empirical: a(n) = 62*a(n-1) - 333*a(n-2) + 396*a(n-3) - 135*a(n-4) for n>5.

Empirical g.f.: x*(5 - 151*x + 276*x^2 - 183*x^3 + 45*x^4) / ((1 - 5*x + 3*x^2)*(1 - 57*x + 45*x^2)). - Colin Barker, Jun 29 2018

A208171 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

15, 2277, 473928, 99752346, 21002874867, 4422202024212, 931104734002155, 196046229442844736, 41277981610623482478, 8691173355900504027213, 1829946411015625966726620, 385299398603702723040648261

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 4 of A208175

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

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

Empirical: a(n) = 226*a(n-1) -3345*a(n-2) +19752*a(n-3) -60897*a(n-4) +108504*a(n-5) -114399*a(n-6) +68040*a(n-7) -18225*a(n-8) for n>9

A208172 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

51, 33831, 26625693, 21002874867, 16567902881244, 13069424064243420, 10309684155118737894, 8132690993759302714128, 6415391762234363693863872, 5060717478941101906268770749, 3992096250836003074558657203441

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 5 of A208175

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

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

Empirical: a(n) = 846*a(n-1) -46537*a(n-2) +1162868*a(n-3) -17173907*a(n-4) +166807056*a(n-5) -1125592122*a(n-6) +5444000730*a(n-7) -19238506974*a(n-8) +50296239144*a(n-9) -97844056164*a(n-10) +140881555908*a(n-11) -146587250745*a(n-12) +104533491168*a(n-13) -46130948685*a(n-14) +10416243600*a(n-15) -863591625*a(n-16) for n>17

A208173 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

187, 506493, 1496307201, 4422202024212, 13069424064243420, 38625516979536823947, 114154269785454920027391, 337372761040287875038964700, 997075099388051313174129747636

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 6 of A208175

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

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

A208174 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

715, 7594479, 84091222866, 931104734002155, 10309684155118737894, 114154269785454920027391, 1263976383376771173195964686, 13995414281804368959953485044237, 154964620775524737157861783733965485

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 7 of A208175

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

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

cp's OEIS Frontend

A208169 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208170 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208171 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208172 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208173 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208174 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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