A208258 -id:A208258 - cp's OEIS frontend

A208252 Number of n X n 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

1, 12, 2040, 2445264, 20662697664, 1230875651548608, 516901401841519506624, 1530268623239822606574667872, 31936997040921403605588139690977984, 4698799611233642481043318409392291549604736

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Diagonal of A208258

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

R. H. Hardin, Table of n, a(n) for n = 1..13

A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

5, 96, 2040, 43344, 920928, 19566912, 415737216, 8833148160, 187677464064, 3987573838848, 84723785029632, 1800122089230336, 38247105402593280, 812634365429366784, 17266002353004576768, 366849901919230820352

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 3 of A208258.

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

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

Cf. A208258.

Empirical: a(n) = 22*a(n-1) - 16*a(n-2) for n>3.
Conjectures from Colin Barker, Jun 29 2018: (Start)
G.f.: x*(1 - 2*x)*(5 - 4*x) / (1 - 22*x + 16*x^2).
a(n) = (1/32)*sqrt(3/35)*((11-sqrt(105))^n*(-13+sqrt(105)) + (11+sqrt(105))^n*(13+sqrt(105))) for n>1.
(End)

A208254 Number of n X 4 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

14, 768, 43344, 2445264, 137947632, 7782199824, 439026252912, 24767296501776, 1397226183866736, 78823339024454928, 4446752320207192176, 250859789016717819408, 14152043831975777230704, 798375640062491402594064

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 4 of A208258.

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

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

Cf. A208258.

Empirical: a(n) = 61*a(n-1) - 266*a(n-2) + 416*a(n-3) - 256*a(n-4) for n>5.

Empirical g.f.: 2*x*(7 - 43*x + 110*x^2 - 128*x^3 + 64*x^4) / (1 - 61*x + 266*x^2 - 416*x^3 + 256*x^4). - Colin Barker, Jun 29 2018

A208255 Number of nX5 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

41, 6144, 920928, 137947632, 20662697664, 3094987890864, 463586569433280, 69438884409258336, 10400988693344761104, 1557924881981189122032, 233355694295516814615312, 34953469637696859885114528

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 5 of A208258

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

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

Empirical: a(n) = 171*a(n-1) -3370*a(n-2) +29805*a(n-3) -149108*a(n-4) +447784*a(n-5) -778496*a(n-6) +649216*a(n-7) -114688*a(n-8) for n>9

A208256 Number of nX6 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

122, 49152, 19566912, 7782199824, 3094987890864, 1230875651548608, 489518751475118880, 194681408759751734640, 77424717204435400421520, 30791778589670316720418080, 12245877840416847143166208896

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 6 of A208258

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

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

Empirical: a(n) = 483*a(n-1) -37260*a(n-2) +1406078*a(n-3) -32825379*a(n-4) +522499249*a(n-5) -5935275892*a(n-6) +48955308778*a(n-7) -292045494268*a(n-8) +1227794612112*a(n-9) -3438890819616*a(n-10) +5747863337984*a(n-11) -4538037229568*a(n-12) +808526872576*a(n-13) +1304252383232*a(n-14) -1133951057920*a(n-15) +395539644416*a(n-16) -52613349376*a(n-17) for n>18

A208257 Number of nX7 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

Original entry on oeis.org

365, 393216, 415737216, 439026252912, 463586569433280, 489518751475118880, 516901401841519506624, 545815772261840889783840, 576347550907375513255891248, 608587212579607572737693478288

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 7 of A208258

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

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

Empirical: a(n) = 1373*a(n-1) -382385*a(n-2) +54747930*a(n-3) -5050986386*a(n-4) +332267679041*a(n-5) -16472142082703*a(n-6) +636007583672478*a(n-7) -19508251954601454*a(n-8) +480569383283952657*a(n-9) -9546208348531626993*a(n-10) +152598952268814061851*a(n-11) -1946846244225175080346*a(n-12) +19518911243309328077698*a(n-13) -150002896733353526035184*a(n-14) +849776274453519925228352*a(n-15) -3327166677806732426576264*a(n-16) +7899544532604413646690344*a(n-17) -6508673827964553701633600*a(n-18) -20940104457639861466791296*a(n-19) +72463799516214011378881024*a(n-20) -61429017906552923870936064*a(n-21) -129536619155578798140518400*a(n-22) +380737956559758296779800576*a(n-23) -211491273596407625450717184*a(n-24) -649598231455057371522924544*a(n-25) +1411628961483792374550233088*a(n-26) -535856510128456063711707136*a(n-27) -2479363142583076923579039744*a(n-28) +5970652384046936507902066688*a(n-29) -7499573050858256420655071232*a(n-30) +6280307951272279750928760832*a(n-31) -3675985493399257320121171968*a(n-32) +1481320042982141475269115904*a(n-33) -383743024338594997911683072*a(n-34) +54171200367877184095780864*a(n-35) -2546711369956156422225920*a(n-36) for n>37

cp's OEIS Frontend

A208252 Number of n X n 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208253 Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208254 Number of n X 4 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208255 Number of nX5 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208256 Number of nX6 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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A208257 Number of nX7 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

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