A205318 -id:A205318 - cp's OEIS frontend

A205311 Number of (n+1) X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

8, 84, 2606, 193664, 33865634, 13956665238, 13574876544398, 31191658416342676, 169426507164530254382, 2176592549084872196370726, 66158464020552857153017287242, 4759146677426447759184119036493678

Offset: 1

R. H. Hardin Jan 25 2012

nonn

Diagonal of A205318.

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

R. H. Hardin, Table of n, a(n) for n = 1..14

Cf. A205318.

A205312 Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

20, 84, 376, 1708, 7784, 35500, 161928, 738636, 3369320, 15369324, 70107976, 319801228, 1458790184, 6654348460, 30354161928, 138462112716, 631602239720, 2881086973164, 13142230386376, 59948977985548, 273460429154984

Offset: 1

R. H. Hardin, Jan 25 2012

nonn

Column 2 of A205318.

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

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

Cf. A205318.

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

Empirical g.f.: 4*x*(5 - 9*x + 3*x^2) / ((1 - x)*(1 - 5*x + 2*x^2)). - Colin Barker, Jun 11 2018

A205313 Number of (n+1) X 4 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

56, 376, 2606, 18152, 126536, 882182, 6150512, 42881096, 298965278, 2084374136, 14532174632, 101317751318, 706383387200, 4924877262824, 34336051065326, 239389600968776, 1669014906316040, 11636306448704678, 81127872049414160

Offset: 1

R. H. Hardin, Jan 25 2012

nonn

Column 3 of A205318.

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

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

Cf. A205318.

Empirical: a(n) = 10*a(n-1) -24*a(n-2) +21*a(n-3) -6*a(n-4).

Empirical g.f.: 2*x*(2 - 3*x)*(14 - 25*x + 10*x^2) / ((1 - x)*(1 - 9*x + 15*x^2 - 6*x^3)). - Colin Barker, Jun 11 2018

A205314 Number of (n+1) X 5 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

164, 1708, 18152, 193664, 2068148, 22091516, 235994088, 2521075824, 26932295140, 287714402188, 3073619242616, 32835119205664, 350773799961748, 3747276188396572, 40031720975324552, 427654276187965520

Offset: 1

R. H. Hardin, Jan 25 2012

nonn

Column 4 of A205318.

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

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

Cf. A205318.

Empirical: a(n) = 17*a(n-1) -81*a(n-2) +157*a(n-3) -140*a(n-4) +56*a(n-5) -8*a(n-6).

Empirical g.f.: 4*x*(41 - 270*x + 600*x^2 - 580*x^3 + 244*x^4 - 36*x^5) / ((1 - x)*(1 - 16*x + 65*x^2 - 92*x^3 + 48*x^4 - 8*x^5)). - Colin Barker, Jun 11 2018

A205315 Number of (n+1)X6 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

488, 7784, 126536, 2068148, 33865634, 554916092, 9094954742, 149077423220, 2443638951908, 40055966781734, 656597489663162, 10762963773161732, 176426890096852634, 2891996520924867398, 47405724154180563434

Offset: 1

R. H. Hardin Jan 25 2012

nonn

Column 5 of A205318

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

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

Empirical: a(n) = 31*a(n-1) -321*a(n-2) +1569*a(n-3) -4179*a(n-4) +6420*a(n-5) -5671*a(n-6) +2668*a(n-7) -516*a(n-8)

A205316 Number of (n+1)X7 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

1460, 35500, 882182, 22091516, 554916092, 13956665238, 351210375464, 8839958693704, 222522561716050, 5601638723985320, 141014378310113564, 3549888849256712462, 89364987835152404176, 2249679176828409331216

Offset: 1

R. H. Hardin Jan 25 2012

nonn

Column 6 of A205318

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

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

Empirical: a(n) = 56*a(n-1) -1164*a(n-2) +12439*a(n-3) -78536*a(n-4) +314610*a(n-5) -829844*a(n-6) +1464316*a(n-7) -1728640*a(n-8) +1345964*a(n-9) -671600*a(n-10) +205552*a(n-11) -36416*a(n-12) +3392*a(n-13) -128*a(n-14)

A205317 Number of (n+1)X8 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

Original entry on oeis.org

4376, 161928, 6150512, 235994088, 9094954742, 351210375464, 13574876544398, 524918733085720, 20301876944832818, 785274659708798830, 30375704525543067782, 1175006427763697066728, 45452565752953792429196

Offset: 1

R. H. Hardin Jan 25 2012

nonn

Column 7 of A205318

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

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

Empirical: a(n) = 106*a(n-1) -4578*a(n-2) +110127*a(n-3) -1685691*a(n-4) +17662632*a(n-5) -132490685*a(n-6) +732439565*a(n-7) -3041749572*a(n-8) +9607185471*a(n-9) -23244897123*a(n-10) +43214022033*a(n-11) -61676422325*a(n-12) +67255934696*a(n-13) -55515488409*a(n-14) +34166147646*a(n-15) -15313024644*a(n-16) +4816467696*a(n-17) -999456992*a(n-18) +121777664*a(n-19) -6527616*a(n-20)

cp's OEIS Frontend

A205311 Number of (n+1) X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205312 Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205313 Number of (n+1) X 4 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205314 Number of (n+1) X 5 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205315 Number of (n+1)X6 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205316 Number of (n+1)X7 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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A205317 Number of (n+1)X8 0..1 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

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