A184673 -id:A184673 - cp's OEIS frontend

A184665 Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock summing to less than 6.

150, 1740, 19269, 216912, 2430631, 27278035, 305991368, 3432961182, 38513146024, 432071200891, 4847297854288, 54380688812185, 610083824961241, 6844384156411424, 76785501492801006, 861438105302681684

Offset: 1

R. H. Hardin, Jan 19 2011

nonn

Column 1 of A184673.

			Some solutions for 3 X 2:
..0..1....0..0....2..0....2..1....3..2....0..2....1..3....3..1....3..0....3..1
..2..3....3..3....3..3....2..1....1..3....3..3....3..1....3..1....2..3....3..3
..0..1....2..0....3..3....1..2....2..2....2..1....3..1....3..1....2..1....1..0

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

Cf. A184673.

Empirical: a(n) = 10*a(n-1) + 25*a(n-2) - 123*a(n-3) - 73*a(n-4) + 304*a(n-5) + 36*a(n-6) - 144*a(n-7).

Empirical g.f.: x*(150 + 240*x - 1881*x^2 - 828*x^3 + 4756*x^4 + 432*x^5 - 2304*x^6) / (1 - 10*x - 25*x^2 + 123*x^3 + 73*x^4 - 304*x^5 - 36*x^6 + 144*x^7). - Colin Barker, Feb 27 2018

A184666 Number of (n+1)X3 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

1740, 67330, 2405797, 88458672, 3225439429, 117938741095, 4308670152724, 157454260497016, 5753418267657560, 210237556594325891, 7682287249431007868, 280719194120503850605, 10257776899125672523995, 374830158857789457998588

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 2 of A184673

			Some solutions for 5X3
..0..2..2....0..2..2....0..2..2....0..2..0....0..2..0....0..2..2....0..2..2
..2..2..2....2..2..2....2..2..2....2..2..3....2..2..2....2..2..0....2..2..3
..2..1..1....2..2..1....0..3..0....2..0..3....2..2..3....2..2..3....2..0..3
..0..3..2....1..3..3....0..3..3....3..1..3....2..3..1....3..3..1....1..3..0
..3..0..3....3..1..1....0..3..0....0..2..0....3..3..0....2..1..2....3..2..1

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

Empirical: a(n)=33*a(n-1)+254*a(n-2)-4528*a(n-3)-4583*a(n-4)+136276*a(n-5)-51684*a(n-6)-1465238*a(n-7)+1162805*a(n-8)+7140128*a(n-9)-6753172*a(n-10)-16991713*a(n-11)+16867228*a(n-12)+20582754*a(n-13)-20497813*a(n-14)-13213038*a(n-15)+12962168*a(n-16)+4464952*a(n-17)-4283552*a(n-18)-731808*a(n-19)+687168*a(n-20)+44928*a(n-21)-41472*a(n-22)

A184667 Number of (n+1)X4 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

19269, 2405797, 266060160, 30765364899, 3509487618613, 402221585928132, 46028365937520330, 5269979734803579913, 603279614829234560146, 69064202595023175071177, 7906407074804511304606829

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 3 of A184673

			Some solutions for 3X4
..0..2..0..0....2..2..0..1....0..2..2..1....2..2..2..2....2..2..2..1
..2..2..3..3....3..2..3..2....3..2..2..2....3..0..3..2....2..2..2..1
..3..3..3..3....1..1..2..3....2..3..2..3....3..2..3..1....1..3..0..3

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

A184668 Number of (n+1)X5 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

216912, 88458672, 30765364899, 11348244616180, 4110692224930359, 1498459859767029015, 545098899148923125052, 198432026871542606565562, 72218093862175663215790336, 26285411777044349448747311771

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 4 of A184673

			Some solutions for 3X5
..0..0..2..3..1....0..0..2..3..2....0..0..2..0..1....0..0..2..2..0
..3..3..2..3..3....3..3..2..2..3....3..3..2..2..3....3..3..2..3..1
..0..0..3..0..2....1..0..1..2..0....0..0..2..3..0....1..0..2..1..1

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

A184669 Number of (n+1)X6 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

2430631, 3225439429, 3509487618613, 4110692224930359, 4705518067315949795, 5429971895805945122143, 6249280647180715433706216, 7198790025550990326313861165, 8290014690133607000371667238201

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 5 of A184673

			Some solutions for 3X6
..0..0..2..0..3..0....0..0..2..0..3..1....0..0..2..0..3..1....0..0..2..0..2..3
..3..3..3..1..2..3....3..3..3..1..3..2....3..3..3..1..3..3....3..3..3..1..3..3
..2..1..3..1..2..0....2..0..1..3..3..2....2..1..2..2..1..1....1..2..0..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..165

A184670 Number of (n+1)X7 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

27278035, 117938741095, 402221585928132, 1498459859767029015, 5429971895805945122143, 19869188673828370548366580, 72469574283521150229737165516, 264615725211389828099780842721919

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 6 of A184673

			Some solutions for 3X7
..0..0..0..2..0..1..1....0..0..0..0..2..1..2....0..0..0..2..2..2..3
..3..3..3..2..3..2..2....3..3..3..3..2..3..0....3..3..3..2..0..3..2
..0..0..0..1..2..2..2....0..0..0..0..3..3..2....0..0..0..3..3..2..2

R. H. Hardin, Table of n, a(n) for n = 1..58

A184671 Number of (n+1)X8 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

305991368, 4308670152724, 46028365937520330, 545098899148923125052, 6249280647180715433706216, 72469574283521150229737165516, 837185450907978354702239657652981, 9684133255072575015900450075888762942

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 7 of A184673

			Some solutions for 3X8
..0..0..0..0..2..1..0..3....0..0..0..0..2..1..3..3....0..0..0..0..2..3..0..3
..3..3..3..3..2..3..2..3....3..3..3..3..2..2..3..1....3..3..3..3..2..3..1..2
..0..0..0..0..2..1..1..1....0..0..0..0..2..3..2..3....0..0..0..0..2..2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..12

A184664 Number of (n+1)X(n+1) 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

150, 67330, 266060160, 11348244616180, 4705518067315949795, 19869188673828370548366580, 837185450907978354702239657652981

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Diagonal of A184673

			Some solutions for 3X3
..3..3..1....1..0..1....1..2..2....1..3..3....3..1..3....1..1..3....3..1..2
..0..3..2....3..3..2....2..1..3....1..2..2....2..3..3....3..3..2....3..2..3
..3..1..2....3..3..2....2..1..3....2..1..1....1..2..3....2..3..3....3..2..1

A184672 Number of (n+1)X9 0..3 arrays with no 2X2 subblock summing to less than 6.

Original entry on oeis.org

3432961182, 157454260497016, 5269979734803579913, 198432026871542606565562, 7198790025550990326313861165, 264615725211389828099780842721919, 9684133255072575015900450075888762942

Offset: 1

R. H. Hardin Jan 19 2011

nonn

Column 8 of A184673

			Some solutions for 3X9
..0..2..0..2..2..2..2..2..0....0..2..0..2..2..2..0..2..3
..2..3..1..3..0..2..3..2..3....2..3..1..3..0..2..2..3..1
..0..2..0..2..2..2..3..2..0....0..2..0..2..2..3..2..1..2

cp's OEIS Frontend

A184665 Number of (n+1) X 2 0..3 arrays with no 2 X 2 subblock summing to less than 6.

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A184666 Number of (n+1)X3 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184667 Number of (n+1)X4 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184668 Number of (n+1)X5 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184669 Number of (n+1)X6 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184670 Number of (n+1)X7 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184671 Number of (n+1)X8 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184664 Number of (n+1)X(n+1) 0..3 arrays with no 2X2 subblock summing to less than 6.

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A184672 Number of (n+1)X9 0..3 arrays with no 2X2 subblock summing to less than 6.

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