A198715 -id:A198715 - cp's OEIS frontend

A198710 Number of n X 3 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

2, 25, 401, 6548, 107042, 1749965, 28609241, 467717288, 7646461682, 125007943505, 2043688517681, 33411178843628, 546221629207922, 8929887496964645, 145989990956749721, 2386712874803449568, 39019101990629849762

Offset: 1

R. H. Hardin, Oct 29 2011

nonn

Column 3 of A198715.

			Some solutions with all values from 0 to 3 for n=4:
..0..1..2....0..1..2....0..1..0....0..1..2....0..1..0....0..1..2....0..1..0
..2..0..3....2..3..1....1..0..1....3..2..3....2..0..2....2..3..0....1..2..3
..0..1..0....0..1..2....0..2..3....2..3..0....0..3..1....0..2..1....3..0..1
..3..2..3....3..2..1....3..0..1....1..2..3....2..1..3....1..0..3....0..3..2

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

Cf. A198715.

Empirical: a(n) = 19*a(n-1) - 45*a(n-2) + 27*a(n-3).

Empirical g.f.: x*(2 - 13*x + 16*x^2) / ((1 - x)*(1 - 18*x + 27*x^2)). - Colin Barker, Mar 02 2018

A198709 Number of n X n 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

1, 4, 401, 250031, 851787199, 15835552812749, 1606578861528554441, 889483369334451647489771, 2687450673445984030296455830409

Offset: 1

R. H. Hardin Oct 29 2011

nonn

Diagonal of A198715

			Some solutions with all values from 0 to 3 for n=4
..0..1..0..1....0..1..0..2....0..1..0..1....0..1..0..2....0..1..2..0
..1..2..1..3....1..2..1..3....1..0..2..3....2..3..2..3....1..0..3..1
..2..1..3..2....2..1..3..2....2..3..1..2....1..2..0..1....0..3..1..2
..1..3..1..0....1..2..0..1....3..0..2..1....2..0..3..0....2..1..2..3

Jean-François Alcover, Table of n, a(n) for n = 1..16

A198715 = Import["https://oeis.org/A198715/b198715.txt", "Table"][[All, 2]];
a[n_] := A198715[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 16}] (* Jean-François Alcover, Sep 23 2019 *)

A198711 Number of n X 4 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

5, 172, 6548, 250031, 9548295, 364637102, 13925032958, 531779578441, 20307996787865, 775536991678112, 29616787512285048, 1131028064429979731, 43192546862380323515, 1649469330720040937602, 62991170251091380482818

Offset: 1

R. H. Hardin, Oct 29 2011

nonn

Column 4 of A198715.

			Some solutions with all values from 0 to 3 for n=5:
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..1..0..2..0....1..0..1..2....1..0..1..2....1..0..1..0....1..0..1..0
..0..2..0..3....2..1..3..1....3..1..0..1....2..1..0..3....2..1..3..1
..2..1..2..0....1..2..0..3....1..0..3..0....3..2..1..0....3..0..1..3
..1..2..1..2....2..3..1..2....2..1..0..1....2..1..3..2....2..3..0..1

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

Cf. A198715.

Empirical: a(n) = 46*a(n-1) - 312*a(n-2) + 530*a(n-3) - 263*a(n-4).

Empirical g.f.: x*(5 - 58*x + 196*x^2 - 163*x^3) / ((1 - x)*(1 - 45*x + 267*x^2 - 263*x^3)). - Colin Barker, Mar 02 2018

A198712 Number of nX5 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

14, 1201, 107042, 9548295, 851787199, 75987485516, 6778819400772, 604736581320925, 53948385378521909, 4812720805166620356, 429341516830025751982, 38301440209010857426775, 3416861087749979581617789

Offset: 1

R. H. Hardin Oct 29 2011

nonn

Column 5 of A198715

			Some solutions with all values from 0 to 3 for n=4
..0..1..2..0..2....0..1..2..3..1....0..1..0..2..0....0..1..2..0..1
..1..0..3..2..3....1..0..3..1..0....1..0..1..0..1....1..0..1..2..3
..0..1..2..3..1....0..1..2..3..2....0..1..2..1..3....0..1..0..3..1
..1..3..0..2..3....1..2..1..2..1....1..3..0..3..2....1..0..2..1..0

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

Empirical: a(n) = 119*a(n-1) -2929*a(n-2) +25066*a(n-3) -76115*a(n-4) -887*a(n-5) +324153*a(n-6) -444798*a(n-7) +175392*a(n-8)

A198713 Number of nX6 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

41, 8404, 1749965, 364637102, 75987485516, 15835552812749, 3300094936852775, 687733321797971342, 143322307142433346196, 29868095632655586533219, 6224454258216624967544685, 1297164418016611898106044912

Offset: 1

R. H. Hardin Oct 29 2011

nonn

Column 6 of A198715

			Some solutions with all values from 0 to 3 for n=4
..0..1..0..1..0..2....0..1..0..2..3..0....0..1..0..2..0..3....0..1..0..2..1..2
..1..0..2..3..2..3....1..0..2..0..1..2....1..0..2..0..1..2....1..0..2..0..2..3
..0..1..0..2..3..2....0..1..0..2..0..3....0..1..0..1..0..3....0..1..0..1..0..2
..1..0..1..3..1..3....1..0..3..0..2..0....1..0..2..0..3..2....1..0..3..2..1..3

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

Empirical: a(n) = 313*a(n-1) -25836*a(n-2) +915863*a(n-3) -16213670*a(n-4) +144756201*a(n-5) -517271096*a(n-6) -1142631169*a(n-7) +16130100519*a(n-8) -49834494904*a(n-9) +41222570902*a(n-10) +81411834252*a(n-11) -186980689770*a(n-12) +120589827444*a(n-13) -21008679048*a(n-14)

A198714 Number of nX7 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

122, 58825, 28609241, 13925032958, 6778819400772, 3300094936852775, 1606578861528554441, 782129027546108478208, 380763168247444298026697, 185366606445710896112671190, 90241867886483759053800200221

Offset: 1

R. H. Hardin Oct 29 2011

nonn

Column 7 of A198715

			Some solutions with all values from 0 to 3 for n=4
..0..1..0..2..0..1..2....0..1..0..2..0..3..0....0..1..0..2..1..3..1
..1..0..2..0..2..3..1....1..0..2..0..2..1..3....1..0..2..0..3..1..0
..0..1..0..2..1..2..0....0..1..0..2..0..3..1....0..1..0..2..1..0..3
..1..0..2..0..3..1..2....1..0..2..0..3..0..3....1..0..2..0..2..3..1

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

Empirical: a(n) = 820*a(n-1) -205689*a(n-2) +23977335*a(n-3) -1448890080*a(n-4) +40681354716*a(n-5) +113470351405*a(n-6) -45083135350759*a(n-7) +1384281526165416*a(n-8) -16268081626571563*a(n-9) -63890727017432669*a(n-10) +4141584863538946248*a(n-11) -41819886892303325457*a(n-12) -30483804619910407683*a(n-13) +3863177257558021068078*a(n-14) -27574675558592643871665*a(n-15) -5974253069771812381395*a(n-16) +994204560645628682891988*a(n-17) -4133294712546191129276631*a(n-18) -5200219344858789634094007*a(n-19) +79782056692975632581941806*a(n-20) -145976694071885459756226729*a(n-21) -381423099164490179830401489*a(n-22) +1687752294947845021038392100*a(n-23) -947863788801858331624770840*a(n-24) -4416578720165084280803867511*a(n-25) +7519754083669273956859949007*a(n-26) -393515001351016977961508328*a(n-27) -8318760918675594342013626309*a(n-28) +7729370069736269915861360652*a(n-29) -2679235928159828068047490236*a(n-30) +224133015493782945421410924*a(n-31) +60130490872795258151715444*a(n-32) -9198797534128825159826898*a(n-33)

cp's OEIS Frontend

A198710 Number of n X 3 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198709 Number of n X n 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198711 Number of n X 4 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198712 Number of nX5 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198713 Number of nX6 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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A198714 Number of nX7 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.

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