A269097 -id:A269097 - cp's OEIS frontend

A269091 Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

4, 96, 1152, 11424, 103488, 889056, 7375872, 59698464, 474360768, 3715826016, 28777886592, 220814937504, 1681292682048, 12718165610976, 95670977133312, 716203564928544, 5338972029467328, 39651633731043936, 293513242790716032

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 2 of A269097.

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

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

Cf. A269097.

Empirical: a(n) = 14*a(n-1) -49*a(n-2) for n>3.
Conjectures from Colin Barker, Mar 21 2018: (Start)
G.f.: 4*x*(1 + 10*x + x^2) / (1 - 7*x)^2.
a(n) = 96*7^(n-3)*(5*n-3) for n>1.
(End)

A269090 Number of n X n 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

0, 96, 31296, 37963968, 211625837280, 5826856525990272, 819944297332124826720, 600994567853371717147309536, 2321584677123190401202986846749664, 47631920426007575412576023256743509016160

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Diagonal of A269097.

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

R. H. Hardin, Table of n, a(n) for n = 1..11

Cf. A269097.

A269092 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

24, 1152, 31296, 715320, 15024096, 300056400, 5795398368, 109294975080, 2024660774592, 36988673403168, 668280340085760, 11964667932759960, 212595089870143008, 3753382504394332656, 65903307050002080672

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 3 of A269097.

Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>5.

Empirical g.f.: 24*x*(1 + 12*x - 46*x^2 + 33*x^3 + 9*x^4) / (1 - 18*x + 27*x^2)^2. - Colin Barker, Jan 19 2019

A269093 Number of nX4 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

108, 11424, 715320, 37963968, 1856325000, 86415197088, 3892946216856, 171307237216320, 7406621052177000, 315868041326151072, 13323538607075686392, 556962735401445373632, 23108630644746952831560

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 4 of A269097.

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

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

Cf. A269097.

Empirical: a(n) = 90*a(n-1) -2559*a(n-2) +24556*a(n-3) -94959*a(n-4) +140442*a(n-5) -69169*a(n-6) for n>7

A269094 Number of nX5 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

432, 103488, 15024096, 1856325000, 211625837280, 22984646281176, 2416707037884480, 248267055360211392, 25062609875880382656, 2495854741014485439624, 245851383088389214772304

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 5 of A269097.

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

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

Cf. A269097.

Empirical: a(n) = 236*a(n-1) -19546*a(n-2) +707906*a(n-3) -13261621*a(n-4) +137719076*a(n-5) -784626841*a(n-6) +2025590366*a(n-7) +1091882414*a(n-8) -18874661724*a(n-9) +33829878231*a(n-10) +10605114324*a(n-11) -91783964484*a(n-12) +94503314304*a(n-13) -30762353664*a(n-14) for n>15

A269095 Number of nX6 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

1620, 889056, 300056400, 86415197088, 22984646281176, 5826856525990272, 1430390977786967280, 343122372255163660560, 80890546793429923552008, 18813147168685841982033408, 4328190538478506032118840320

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 6 of A269097.

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

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

Cf. A269097.

Empirical: a(n) = 624*a(n-1) -148392*a(n-2) +17707654*a(n-3) -1237692774*a(n-4) +55270649556*a(n-5) -1656470723141*a(n-6) +34132157660412*a(n-7) -484096890617541*a(n-8) +4569992373952272*a(n-9) -25146261177957786*a(n-10) +25694778316842858*a(n-11) +756190434082200840*a(n-12) -6052462771631752224*a(n-13) +18126128855859433455*a(n-14) +18664609483184919500*a(n-15) -342070453287924453888*a(n-16) +1141375792492508055684*a(n-17) -1231488788816842507708*a(n-18) -2418565901590843869576*a(n-19) +9095171580512370570684*a(n-20) -8677540039273932904920*a(n-21) -4965678440542161492372*a(n-22) +17155105764294227912496*a(n-23) -13588702943203699236720*a(n-24) +4184136771765648014016*a(n-25) -441364595341874186304*a(n-26) for n>27

A269096 Number of nX7 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

Original entry on oeis.org

5832, 7375872, 5795398368, 3892946216856, 2416707037884480, 1430390977786967280, 819944297332124826720, 459338963193935894366016, 252910225839761737259917296, 137383600294764153686560207128

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 7 of A269097.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Cf. A269097.

Empirical recurrence of order 64 (see link above)

cp's OEIS Frontend

A269091 Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269090 Number of n X n 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269092 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269093 Number of nX4 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269094 Number of nX5 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269095 Number of nX6 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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A269096 Number of nX7 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

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