A231263 -id:A231263 - cp's OEIS frontend

A231257 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

3, 15, 89, 547, 3381, 20911, 129329, 799835, 4946509, 30591143, 189187465, 1170008467, 7235785189, 44748896799, 276744502881, 1711495152971, 10584548667901, 65458946997783, 404823472069561, 2503585087356803

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 2 of A231263.

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

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

Empirical: a(n) = 10*a(n-1) -29*a(n-2) +36*a(n-3) -16*a(n-4).

Empirical g.f.: x*(1 - 2*x)*(3 - 9*x + 8*x^2) / ((1 - x)*(1 - 9*x + 20*x^2 - 16*x^3)). - Colin Barker, Feb 16 2018

A231258 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

4, 32, 304, 2982, 29366, 289230, 2848550, 28054534, 276301638, 2721223974, 26800640678, 263952669990, 2599602461350, 25602820961958, 252155647340198, 2483416596612262, 24458536057349286, 240885877498412198

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 3 of A231263.

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

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

Empirical: a(n) = 17*a(n-1) -96*a(n-2) +308*a(n-3) -628*a(n-4) +800*a(n-5) -656*a(n-6) +256*a(n-7).

Empirical g.f.: 2*x*(2 - 18*x + 72*x^2 - 173*x^3 + 256*x^4 - 228*x^5 + 128*x^6) / ((1 - x)*(1 - 16*x + 80*x^2 - 228*x^3 + 400*x^4 - 400*x^5 + 256*x^6)). - Colin Barker, Feb 16 2018

A231259 Number of (n+1)X(4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

7, 83, 1253, 19503, 302121, 4670875, 72212345, 1116538567, 17264116873, 266940042371, 4127456101305, 63819175744751, 986779131942921, 15257688013347083, 235916058283574201, 3647760162012484183

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 4 of A231263

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

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

Empirical: a(n) = 31*a(n-1) -364*a(n-2) +2570*a(n-3) -12609*a(n-4) +44731*a(n-5) -117554*a(n-6) +227260*a(n-7) -319008*a(n-8) +314816*a(n-9) -208992*a(n-10) +83456*a(n-11) -14336*a(n-12)

A231260 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

12, 211, 5109, 126851, 3130708, 77333664, 1911322499, 47238533054, 1167469879103, 28853204049176, 713087755664766, 17623492910180119, 435552963190637813, 10764403103144565858, 266035096373745526067

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 5 of A231263

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

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

Empirical: a(n) = 69*a(n-1) -2078*a(n-2) +38960*a(n-3) -525899*a(n-4) +5498915*a(n-5) -46432883*a(n-6) +324971505*a(n-7) -1918092860*a(n-8) +9666311433*a(n-9) -41987092645*a(n-10) +158405641708*a(n-11) -522483149728*a(n-12) +1515303637316*a(n-13) -3883210245412*a(n-14) +8829280197296*a(n-15) -17868610021296*a(n-16) +32259257306496*a(n-17) -52016416190400*a(n-18) +74922164013056*a(n-19) -96301233124608*a(n-20) +110211044965376*a(n-21) -111885000085504*a(n-22) +100202065260544*a(n-23) -78553659015168*a(n-24) +53334115090432*a(n-25) -30908302295040*a(n-26) +14987112742912*a(n-27) -5912828837888*a(n-28) +1821821108224*a(n-29) -410773356544*a(n-30) +60196651008*a(n-31) -4294967296*a(n-32)

A231261 Number of (n+1)X(6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

23, 557, 21894, 866396, 34170727, 1350570015, 53369789699, 2108712981800, 83318930054700, 3292096503338981, 130077252787397712, 5139609041198810834, 203076105223297844491, 8023938109223922493851, 317041646252827399145319

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 6 of A231263

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 67

Empirical recurrence of order 67 (see link above)

A231262 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

44, 1471, 94234, 5921588, 373664749, 23652344858, 1496478177166, 94693898367381, 5992336358720087, 379199481911896240, 23995972977026962928, 1518480393702303769523, 96090421103022757089502

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Column 7 of A231263

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

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

A231264 Number of (2+1) X (n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

6, 15, 32, 83, 211, 557, 1471, 3909, 10387, 27617, 73419, 195197, 518979, 1379897, 3669051, 9755861, 25940515, 68974961, 183402043, 487659661, 1296670403, 3447803113, 9167594299, 24376331077, 64815862051, 172343243361, 458255009275

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Row 2 of A231263.

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

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

Empirical: a(n) = 4*a(n-1) -2*a(n-2) -8*a(n-3) +11*a(n-4) -4*a(n-6) -4*a(n-7) -4*a(n-8) +8*a(n-9).

Empirical g.f.: x*(6 - 9*x - 16*x^2 + 33*x^3 - 3*x^4 - 30*x^5 + x^6 - 2*x^7 + 40*x^8) / ((1 - x)*(1 + x)*(1 - 2*x + 2*x^2)*(1 - 2*x^2)*(1 - 2*x - x^2 - 2*x^3)). - Colin Barker, Feb 16 2018

A231265 Number of (3+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

22, 89, 304, 1253, 5109, 21894, 94234, 411978, 1804685, 7941968, 34969518, 154177482, 679856170, 2999022193, 13230140405, 58371368067, 257539346061, 1136325839478, 5013778949950, 22122400344087, 97611358054570

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Row 3 of A231263

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

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

Empirical: a(n) = 9*a(n-1) -20*a(n-2) -36*a(n-3) +220*a(n-4) -282*a(n-5) -226*a(n-6) +1107*a(n-7) -1331*a(n-8) +254*a(n-9) +1022*a(n-10) -257*a(n-11) -2156*a(n-12) +2602*a(n-13) +2385*a(n-14) -8433*a(n-15) +7492*a(n-16) -959*a(n-17) -1626*a(n-18) -531*a(n-19) -3536*a(n-20) +3860*a(n-21) -2019*a(n-22) +4258*a(n-23) -1660*a(n-24) +328*a(n-25) -368*a(n-26) -96*a(n-27) for n>28

A231266 Number of (4+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

86, 547, 2982, 19503, 126851, 866396, 5921588, 40973953, 283765581, 1972122444, 13710377266, 95395947525, 663770545015, 4619277813951, 32145505935933, 223706188296535, 1556796061665136, 10833978133171498, 75395132198062729

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Row 4 of A231263

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

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

A231267 Number of (5+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

342, 3381, 29366, 302121, 3130708, 34170727, 373664749, 4147016414, 46117392977, 515063996641, 5757867388323, 64448318261860, 721609183551621, 8082185902161731, 90528853400096455, 1014081345152953804

Offset: 1

R. H. Hardin, Nov 06 2013

nonn

Row 5 of A231263

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

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

cp's OEIS Frontend

A231257 Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231258 Number of (n+1) X (3+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231259 Number of (n+1)X(4+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231260 Number of (n+1)X(5+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231261 Number of (n+1)X(6+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231262 Number of (n+1)X(7+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231264 Number of (2+1) X (n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231265 Number of (3+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231266 Number of (4+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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A231267 Number of (5+1)X(n+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.

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