A269052 -id:A269052 - cp's OEIS frontend

A269046 Number of n X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

3, 42, 594, 24192, 1643376, 242861616, 71430596250, 43961616939276, 56121206116838532, 149312689805356303800, 836315757545942679945480, 9777884421682321788379713444, 242268002268280142077867206348378

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Diagonal of A269052.

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

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

Cf. A269052.

A269047 Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

24, 102, 594, 3258, 17346, 90450, 464250, 2353338, 11809746, 58773858, 290465706, 1426996746, 6974700162, 33938314674, 164494914138, 794524032090, 3825755303730, 18370501130754, 87990608484618, 420498562000554

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Column 3 of A269052.

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.: 6*x*(1 - x)*(1 - 2*x)*(4 - 11*x + 4*x^2) / (1 - 5*x + 2*x^2)^2. - Colin Barker, Jan 18 2019

A269048 Number of n X 4 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

60, 360, 3078, 24192, 183072, 1350672, 9779808, 69793968, 492374976, 3441051984, 23861339424, 164375084016, 1125975740544, 7675458754704, 52099028628960, 352309891913520, 2374503933353280, 15956129491021776, 106934858162261664

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Column 4 of A269052.

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*(10 - 80*x + 243*x^2 - 290*x^3 + 105*x^4) / (1 - 7*x + 4*x^2)^2. - Colin Barker, Jan 18 2019

A269049 Number of nX5 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

144, 1068, 13140, 149358, 1643376, 17696520, 187575858, 1964080920, 20365312416, 209472681102, 2140087086852, 21738862087680, 219728193571542, 2211332610944712, 22170082238167692, 221519854346189046

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 5 of A269052.

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

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

Cf. A269052.

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

A269050 Number of n X 6 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

336, 3288, 58752, 971844, 15547380, 242861616, 3726221592, 56376679620, 843461153880, 12504078167988, 183960496250712, 2689028139554232, 39089999874219540, 565531265339620620, 8147584788387401052

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 6 of A269052.

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

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

Cf. A269052.

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.

A269051 Number of nX7 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

768, 9864, 253416, 6053094, 140497512, 3193266318, 71430596250, 1577976495486, 34509932303172, 748499855355192, 16122334931683590, 345226129034011068, 7354858033380328494, 156000244649213353110, 3296017711974478218258

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Column 7 of A269052.

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

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

Cf. A269052.

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

A269053 Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

9, 42, 102, 360, 1068, 3288, 9864, 29472, 87312, 257184, 753504, 2197632, 6383808, 18478464, 53318784, 153414144, 440293632, 1260710400, 3602253312, 10273007616, 29245172736, 83119822848, 235886217216, 668491456512, 1892026552320

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Row 2 of A269052.

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

Empirical g.f.: 3*x*(3 + 2*x - 22*x^2 + 8*x^3) / (1 - 2*x - 2*x^2)^2. - Colin Barker, Jan 18 2019

A269054 Number of 3 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

27, 174, 594, 3078, 13140, 58752, 253416, 1090344, 4637904, 19604352, 82332384, 343986912, 1430547456, 5925418752, 24456120000, 100618925568, 412797979584, 1689208728576, 6896384506176, 28095875422848, 114241910041536

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

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

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

Row 3 of A269052.

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.: 3*x*(9 + 4*x - 141*x^2 + 148*x^3 + 82*x^4 - 38*x^5 - 24*x^6 + 8*x^7) / (1 - 3*x - 4*x^2 + 2*x^3)^2. - Colin Barker, Jan 18 2019

A269055 Number of 4Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

81, 666, 3258, 24192, 149358, 971844, 6053094, 37741920, 231943614, 1417576284, 8599619586, 51899214960, 311654917170, 1863739501308, 11103704855298, 65935768579488, 390381077316294, 2305171593612444, 13579182450069246

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Row 4 of A269052.

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

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

Cf. A269052.

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

A269056 Number of 5Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

Original entry on oeis.org

243, 2430, 17346, 183072, 1643376, 15547380, 140497512, 1273499256, 11354964888, 100764874440, 886829123676, 7765850889120, 67643548943508, 586749197487720, 5069733374448192, 43657996370224608, 374818434125094900

Offset: 1

R. H. Hardin, Feb 18 2016

nonn

Row 5 of A269052.

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

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

Cf. A269052.

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

A269046 Number of n X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269047 Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269048 Number of n X 4 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269049 Number of nX5 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269050 Number of n X 6 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269051 Number of nX7 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269053 Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269054 Number of 3 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269055 Number of 4Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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A269056 Number of 5Xn 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

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