A269035 -id:A269035 - cp's OEIS frontend

A269029 Number of n X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

0, 24, 348, 18384, 1326576, 208867428, 63310818360, 40013955378312, 51911512873697772, 140039775591497709312, 791864652110724378938904, 9334169232033820587188999592, 232675011644185023762453520339476

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Diagonal of A269035.

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

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

Cf. A269035.

A269030 Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

12, 48, 348, 2136, 12228, 67104, 357756, 1867560, 9593844, 48665904, 244357740, 1216672824, 6015296484, 29561944128, 144531868764, 703461546312, 3410368965588, 16475694411600, 79347347565132, 381071870841432

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Column 3 of A269035.

Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n>5.

Empirical g.f.: 12*x*(1 - 6*x + 18*x^2 - 16*x^3 + 4*x^4) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 18 2019

A269031 Number of n X 4 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

36, 216, 2166, 18384, 146064, 1114848, 8277072, 60218112, 431354928, 3052215072, 21383561232, 148585984320, 1025363155440, 7034327057760, 48013557090768, 326276117933952, 2208609401649072, 14899002865010592, 100198549907000208

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Column 4 of A269035.

Empirical: a(n) = 14*a(n-1) - 57*a(n-2) + 56*a(n-3) - 16*a(n-4) for n>5.

Empirical g.f.: 6*x*(6 - 48*x + 199*x^2 - 274*x^3 + 105*x^4) / (1 - 7*x + 4*x^2)^2. - Colin Barker, Jan 18 2019

A269032 Number of nX5 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

96, 672, 9528, 115656, 1326576, 14710368, 159397596, 1698064656, 17853542544, 185754411168, 1916112393912, 19623814814640, 199755193119372, 2022721445384448, 20388967766219208, 204700225563136152

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 5 of A269035.

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

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

Cf. A269035.

Empirical: a(n) = 28*a(n-1) -286*a(n-2) +1290*a(n-3) -2373*a(n-4) +304*a(n-5) +3551*a(n-6) -2846*a(n-7) -546*a(n-8) +1308*a(n-9) -505*a(n-10) +76*a(n-11) -4*a(n-12) for n>13

A269033 Number of nX6 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

240, 2208, 44760, 785124, 13031664, 208867428, 3266423688, 50155587360, 759280601376, 11364951702132, 168545724611088, 2480433137331636, 36267257458624740, 527333427504496308, 7630684978884541020

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 6 of A269035.

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

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

Cf. A269035.

Empirical: a(n) = 36*a(n-1) -436*a(n-2) +1854*a(n-3) +340*a(n-4) -19128*a(n-5) +23849*a(n-6) +56184*a(n-7) -108224*a(n-8) -40816*a(n-9) +160400*a(n-10) -34136*a(n-11) -83203*a(n-12) +42628*a(n-13) +6468*a(n-14) -6334*a(n-15) +204*a(n-16) +240*a(n-17) -25*a(n-18) for n>19

A269034 Number of nX7 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

576, 6912, 198816, 4998648, 119790816, 2783857776, 63310818360, 1416701634552, 31304407671636, 684763778434512, 14854833017622684, 320017408314705960, 6853471478780510820, 146027732878366085832, 3097663460112852295020

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 7 of A269035.

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

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

Cf. A269035.

Empirical: a(n) = 82*a(n-1) -2779*a(n-2) +50254*a(n-3) -514677*a(n-4) +2743554*a(n-5) -2950648*a(n-6) -48609034*a(n-7) +245316224*a(n-8) -89432156*a(n-9) -2444502643*a(n-10) +5704858072*a(n-11) +7254972423*a(n-12) -41716035658*a(n-13) +18035762825*a(n-14) +132606292618*a(n-15) -178302990168*a(n-16) -171928095488*a(n-17) +491624257303*a(n-18) -70904009836*a(n-19) -621985038704*a(n-20) +477824279660*a(n-21) +281672875548*a(n-22) -522707244404*a(n-23) +119050620101*a(n-24) +190519380818*a(n-25) -140300285301*a(n-26) +10246766686*a(n-27) +24709126330*a(n-28) -9478840252*a(n-29) -368991021*a(n-30) +964165580*a(n-31) -172681320*a(n-32) -20355920*a(n-33) +9906636*a(n-34) -719568*a(n-35) -120720*a(n-36) +22272*a(n-37) -1024*a(n-38) for n>39

A269036 Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 24, 48, 216, 672, 2208, 6912, 21408, 65280, 196992, 589056, 1748352, 5156352, 15124992, 44156928, 128383488, 371908608, 1073879040, 3091820544, 8878479360, 25435250688, 72710922240, 207448571904, 590798364672, 1679765078016

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Row 2 of A269035.

Empirical: a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4).

Empirical g.f.: 24*x^2*(1 - x)^2 / (1 - 2*x - 2*x^2)^2. - Colin Barker, Jan 18 2019

A269037 Number of 3 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 120, 348, 2166, 9528, 44760, 198816, 877800, 3809856, 16379232, 69769920, 295055136, 1239952512, 5183031744, 21564442752, 89355535680, 368925874944, 1518322209600, 6230763310464, 25503209969088, 104143201935360

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Row 3 of A269035.

Empirical: a(n) = 6*a(n-1) - a(n-2) - 28*a(n-3) - 4*a(n-4) + 16*a(n-5) - 4*a(n-6) for n>8.

Empirical g.f.: 6*x^2*(20 - 62*x + 33*x^2 + 40*x^3 - 3*x^4 - 16*x^5 + 4*x^6) / (1 - 3*x - 4*x^2 + 2*x^3)^2. - Colin Barker, Jan 18 2019

A269038 Number of 4Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 504, 2136, 18384, 115656, 785124, 4998648, 31834476, 198736752, 1231177296, 7552688064, 46020487500, 278641166280, 1678349335044, 10062618187272, 60089435895360, 357550261665528, 2120806295463156, 12543856834626072

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Row 4 of A269035.

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

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

Cf. A269035.

Empirical: a(n) = 6*a(n-1) +23*a(n-2) -102*a(n-3) -288*a(n-4) +250*a(n-5) +787*a(n-6) -238*a(n-7) -741*a(n-8) +124*a(n-9) +196*a(n-10) -16*a(n-11) -16*a(n-12) for n>14

A269039 Number of 5Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

Original entry on oeis.org

0, 1944, 12228, 146064, 1326576, 13031664, 119790816, 1105914780, 9987532176, 89650751964, 796324353216, 7029528437100, 61650349082232, 537978900955440, 4672818187679448, 40427882184540648, 348530963947264848

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Row 5 of A269035.

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

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

Cf. A269035.

Empirical: a(n) = 12*a(n-1) +26*a(n-2) -566*a(n-3) -123*a(n-4) +8804*a(n-5) -4121*a(n-6) -59620*a(n-7) +55115*a(n-8) +183692*a(n-9) -256127*a(n-10) -211910*a(n-11) +498819*a(n-12) -48036*a(n-13) -371692*a(n-14) +214008*a(n-15) +43848*a(n-16) -64656*a(n-17) +8640*a(n-18) +5184*a(n-19) -1296*a(n-20) for n>22

cp's OEIS Frontend

A269029 Number of n X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269030 Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269031 Number of n X 4 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269032 Number of nX5 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269033 Number of nX6 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269034 Number of nX7 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269036 Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269037 Number of 3 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269038 Number of 4Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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A269039 Number of 5Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

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