A278188 -id:A278188 - cp's OEIS frontend

A278185 Number of nX4 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 136, 13012, 1075258, 91270219, 7737459027, 656008970388, 55620335387114, 4715820197535009, 399835065589298715, 33900377809514573711, 2874274212652455298123, 243697940183994435905588

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Column 4 of A278188.

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

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

Cf. A278188.

A278183 Number of n X 2 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 3, 28, 200, 1532, 11794, 90538, 695252, 5339294, 41003018, 314882364, 2418138526, 18570087298, 142608927356, 1095164819630, 8410314860218, 64586987065356, 495995568270926, 3808996439085090, 29251176423848812

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

			Some solutions for n=4:
..0..1. .0..2. .0..2. .0..1. .0..3. .0..1. .0..3. .0..1. .0..1. .0..3
..3..2. .1..3. .1..3. .3..2. .1..2. .0..2. .1..3. .0..2. .1..2. .1..0
..2..1. .2..0. .1..0. .3..1. .1..0. .3..3. .2..0. .1..3. .0..3. .2..0
..1..1. .3..2. .2..3. .0..3. .3..3. .2..1. .1..0. .3..0. .1..2. .3..1

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

Column 2 of A278188.

Empirical: a(n) = 8*a(n-1) - 4*a(n-2) + 15*a(n-3) - 26*a(n-4) + 14*a(n-5) - 16*a(n-6).

Empirical g.f.: x^2*(3 + 4*x - 12*x^2 - x^3 - 4*x^4) / (1 - 8*x + 4*x^2 - 15*x^3 + 26*x^4 - 14*x^5 + 16*x^6). - Colin Barker, Feb 08 2019

A278184 Number of nX3 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 19, 544, 13720, 347116, 8803344, 223230876, 5660949042, 143557203008, 3640498372990, 92320193797850, 2341167983288042, 59370190792031534, 1505581649925192516, 38180374263992817136, 968224459304580152320

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Column 3 of A278188.

			Some solutions for n=4
..0..2..3. .0..1..0. .0..3..2. .0..1..3. .0..3..2. .0..3..2. .0..2..1
..1..3..0. .0..2..3. .1..0..2. .3..2..0. .1..3..1. .1..2..1. .1..3..2
..2..0..1. .3..2..3. .2..0..2. .2..1..0. .2..1..0. .0..2..1. .0..3..1
..1..3..2. .2..1..0. .3..2..3. .0..1..3. .0..3..2. .3..3..2. .2..3..0

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

Cf. A278188.

Empirical: a(n) = 31*a(n-1) -155*a(n-2) +301*a(n-3) +159*a(n-4) -2992*a(n-5) +9662*a(n-6) -29732*a(n-7) +126855*a(n-8) -280808*a(n-9) -58215*a(n-10) +1824424*a(n-11) -5134012*a(n-12) +7021960*a(n-13) -3782179*a(n-14) -161494*a(n-15) -12931*a(n-16) +1006187*a(n-17) +1090*a(n-18) -1012324*a(n-19) -2180228*a(n-20) +2329252*a(n-21) -1301360*a(n-22) +252136*a(n-23) +383856*a(n-24) +87584*a(n-25) -102976*a(n-26) +3840*a(n-27)

A278186 Number of nX5 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 935, 295190, 81691958, 23124026160, 6545874548694, 1852662745588838, 524386828923495662, 148424784547109672280, 42010806495461042971956, 11890925205860266718183950, 3365660260074301506275917454

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Column 5 of A278188.

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

R. H. Hardin, Table of n, a(n) for n = 1..34

Cf. A278188.

A278189 Number of 2 X n 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 3, 19, 136, 935, 6381, 43478, 296105, 2016307, 13729364, 93484479, 636542307, 4334257038, 29512224731, 200950553535, 1368284654492, 9316734157423, 63438214373401, 431954692843542, 2941205998493005, 20026852048660187

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

			Some solutions for n=4:
..0..1..2..3. .0..2..3..2. .0..2..1..0. .0..1..2..1. .0..1..0..2
..3..2..1..0. .1..1..0..2. .1..3..2..1. .3..1..3..0. .1..2..3..3

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

Row 2 of A278188.

Empirical: a(n) = 9*a(n-1) - 16*a(n-2) + 9*a(n-3) - 12*a(n-4) + 5*a(n-5) + 7*a(n-6) - 4*a(n-7).

Empirical g.f.: x^2*(3 - 2*x)*(1 - x + x^2)^2 / (1 - 9*x + 16*x^2 - 9*x^3 + 12*x^4 - 5*x^5 - 7*x^6 + 4*x^7). - Colin Barker, Feb 08 2019

A278190 Number of 3Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 28, 544, 13012, 295190, 6715738, 152540636, 3464413662, 78677378754, 1786751336003, 40576751391716, 921488781267445, 20926797071937044, 475242697298621311, 10792651081336090474, 245098594252284069018

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Row 3 of A278188.

			Some solutions for n=4
..0..1..1..2. .0..3..2..0. .0..2..3..2. .0..2..1..3. .0..3..2..1
..0..2..0..3. .1..0..2..1. .1..3..0..2. .1..3..1..0. .1..3..0..0
..3..3..3..2. .2..3..3..1. .0..0..1..0. .2..3..0..3. .2..2..2..3

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

Cf. A278188.

Empirical: a(n) = 34*a(n-1) -276*a(n-2) +250*a(n-3) +5297*a(n-4) -20136*a(n-5) +4831*a(n-6) +181378*a(n-7) -1050607*a(n-8) +2611385*a(n-9) +2377130*a(n-10) -24865181*a(n-11) +58571426*a(n-12) -124741804*a(n-13) +39013769*a(n-14) +962725072*a(n-15) -2120258810*a(n-16) +2060359647*a(n-17) -6830682990*a(n-18) +17373603369*a(n-19) -36590870077*a(n-20) +112123187091*a(n-21) -229499868670*a(n-22) +218602997839*a(n-23) -35696895236*a(n-24) -141877021986*a(n-25) +185847138194*a(n-26) -164177014211*a(n-27) +146029335334*a(n-28) -90825738933*a(n-29) +63377392966*a(n-30) -55308439922*a(n-31) +56311709818*a(n-32) -26237133100*a(n-33) +16744394402*a(n-34) -8107373456*a(n-35) +4217643492*a(n-36) -1328832216*a(n-37) +353058936*a(n-38) -437975888*a(n-39) +53293248*a(n-40) -15240960*a(n-41) +1330560*a(n-42) -207360*a(n-43)

A278191 Number of 4Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 200, 13720, 1075258, 81691958, 6196345742, 469577175712, 35577034730206, 2695338849906758, 204197662339944373, 15469874074262345128, 1171986102689397728682, 88788773705648773915186

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Row 4 of A278188.

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

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

Cf. A278188.

A278192 Number of 5Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 1532, 347116, 91270219, 23124026160, 5858713218010, 1482450100931615, 375049865320978231, 94879541460515598902, 24002203229663363493985, 6071950545418789283104046, 1536048854453696521513657702

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Row 5 of A278188.

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

R. H. Hardin, Table of n, a(n) for n = 1..126

Cf. A278188.

A278193 Number of 6Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 11794, 8803344, 7737459027, 6545874548694, 5537142857552112, 4678308031001778581, 3951925612543275997042, 3338154929554215989823146, 2819671588394426773289855424, 2381712111047192598048356777986

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Row 6 of A278188.

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

R. H. Hardin, Table of n, a(n) for n = 1..18

Cf. A278188.

A278187 Number of nX6 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Original entry on oeis.org

0, 6381, 6715738, 6196345742, 5858713218010, 5537142857552112, 5232919178331757631, 4945638025497366239942, 4674127103296221122266834, 4417520697715221210576165981

Offset: 1

R. H. Hardin, Nov 14 2016

nonn

Column 6 of A278188.

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

Cf. A278188.

cp's OEIS Frontend

A278185 Number of nX4 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278183 Number of n X 2 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278184 Number of nX3 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278186 Number of nX5 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278189 Number of 2 X n 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278190 Number of 3Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278191 Number of 4Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278192 Number of 5Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278193 Number of 6Xn 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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A278187 Number of nX6 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

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