A269109 -id:A269109 - cp's OEIS frontend

A269103 Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

16, 180, 1740, 15540, 132300, 1090740, 8787660, 69580980, 543538380, 4200069300, 32167589580, 244542858420, 1847388128460, 13880833735860, 103809654007500, 773174303047860, 5737767196302540, 42443199898890420, 313054205965641420

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 2 of A269109.

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

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

Cf. A269109.

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*(4 - 11*x + x^2) / (1 - 7*x)^2.
a(n) = 60*7^(n-3)*(8*n+5) for n>1.
(End)

A269102 Number of n X n 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

4, 180, 40908, 43964700, 232068730044, 6206909793496236, 858502190008810133292, 622342168717398556687064028, 2386083493285894017930101786679468

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Diagonal of A269109.

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

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

Cf. A269109.

A269104 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

60, 1740, 40908, 872460, 17593092, 342055548, 6482020140, 120520189980, 2208175854948, 39988864047276, 717328864510092, 12766536225007020, 225704408971133124, 3967699804321484124, 69407066832964073964

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

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

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

Column 3 of A269109.

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.: 12*x*(5 - 35*x + 79*x^2 - 69*x^3 + 18*x^4) / (1 - 18*x + 27*x^2)^2. - Colin Barker, Jan 19 2019

A269105 Number of nX4 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

216, 15540, 872460, 43964700, 2085484068, 95166487524, 4227147007836, 184069947098892, 7894012975085748, 334480929126425748, 14034341507370527532, 584107408947764887164, 24145251769444080595908

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 4 of A269109.

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

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

Cf. A269109.

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

A269106 Number of n X 5 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

756, 132300, 17593092, 2085484068, 232068730044, 24808345933548, 2579398703502996, 262780733311913580, 26357371124964908460, 2611360040338484328156, 256155579492309832819860

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 5 of A269109.

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

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

Cf. A269109.

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.

A269107 Number of nX6 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

2592, 1090740, 342055548, 95166487524, 24808345933548, 6206909793496236, 1509593256271433868, 359627971978314972756, 84330282164848323860700, 19529981463869576058830652, 4477577440675705031339912748

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 6 of A269109.

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

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

Cf. A269109.

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

A269108 Number of n X 7 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

8748, 8787660, 6482020140, 4227147007836, 2579398703502996, 1509593256271433868, 858502190008810133292, 478110059855042497842996, 262048541877700400412558012, 141832398849461215193264315676

Offset: 1

R. H. Hardin, Feb 19 2016

nonn

Column 7 of A269109.

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

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

Cf. A269109.

Empirical recurrence of order 64 (see link above).

cp's OEIS Frontend

A269103 Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269102 Number of n X n 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269104 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269105 Number of nX4 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269106 Number of n X 5 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269107 Number of nX6 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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A269108 Number of n X 7 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three no more than once.

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