A184376 -id:A184376 - cp's OEIS frontend

A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

21, 153, 1107, 8019, 58077, 420633, 3046491, 22064643, 159806277, 1157419449, 8382773187, 60713414163, 439725443661, 3184773389433, 23066169329547, 167059976482179, 1209955382858997, 8763272085493593, 63469230958692531

Offset: 1

R. H. Hardin, Jan 12 2011

nonn

Column 1 of A184376.

			Some solutions for 3 X 2 with a(1,1)=0:
..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..2....0..1....0..0
..1..0....2..2....1..1....2..1....0..2....0..0....2..1....0..2....0..1....1..2
..2..0....1..1....2..0....0..0....0..2....0..2....2..2....0..2....0..2....1..0

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

Cf. A184376.

Empirical: a(n) = 6*a(n-1) + 9*a(n-2).
Conjectures from Colin Barker, Feb 27 2018: (Start)
G.f.: 3*x*(7 + 9*x) / (1 - 6*x - 9*x^2).
a(n) = ((3-3*sqrt(2))^n*(-4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).
(End)

A184369 1/3 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

153, 2755, 49235, 880781, 15754461, 281803871, 5040682279, 90163722073, 1612776998193, 28848073268443, 516011408652059, 9230001997285733, 165098940527912805, 2953158641948611223, 52823754874667184367

Offset: 1

R. H. Hardin, Jan 12 2011

nonn

Column 2 of A184376.

			Some solutions for 5 X 3 with a(1,1)=0:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..1..0..2....1..2..2....0..1..0....0..2..2....1..1..1....0..2..0....1..1..0
..1..2..2....0..2..0....1..1..1....1..1..2....1..2..0....1..2..0....1..0..0
..1..2..2....1..1..0....2..1..2....2..1..2....1..1..1....1..2..0....2..2..2
..1..1..1....2..2..2....0..1..0....0..0..0....0..2..0....0..2..1....0..2..0

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

Cf. A184376.

Empirical: a(n) = 17*a(n-1) + 19*a(n-2) - 57*a(n-3) + 18*a(n-4).

Empirical g.f.: x*(153 + 154*x - 507*x^2 + 162*x^3) / (1 - 17*x - 19*x^2 + 57*x^3 - 18*x^4). - Colin Barker, Feb 27 2018

A184370 1/3 the number of (n+1)X4 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

1107, 49235, 2167173, 95528423, 4210059673, 185547841629, 8177524177277, 360402692568245, 15883791500540967, 700035935394350709, 30852225032929689819, 1359729896274471875219, 59926484677950059719491

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 3 of A184376

			Some solutions for 3X4 with a(1,1)=0
..0..0..0..2....0..1..1..1....0..1..0..1....0..0..2..1....0..1..1..1
..1..2..2..2....0..1..1..0....0..1..0..1....1..0..2..1....2..1..2..0
..0..2..2..0....2..2..2..2....1..1..0..0....1..1..2..1....0..0..0..0

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

Empirical: a(n)=38*a(n-1)+302*a(n-2)-1368*a(n-3)-6770*a(n-4)+12666*a(n-5)-575*a(n-6)-5790*a(n-7)+828*a(n-8)+648*a(n-9)

A184371 1/3 the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

8019, 880781, 95528423, 10378244309, 1127256514575, 122443114867993, 13299774554091575, 1444622701339019869, 156915034606615850427, 17044123945719790186817, 1851334139596041020316331

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 4 of A184376.

			Some solutions for 3 X 5 with a(1,1)=0
..0..0..0..1..0....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
..1..2..2..2..0....0..0..2..2..1....0..1..0..1..1....2..2..0..1..2
..1..1..1..1..1....2..1..1..0..0....2..1..0..0..0....0..2..0..1..0

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

Cf. A184376.

Empirical: a(n)=114*a(n-1)-197*a(n-2)-44924*a(n-3)+280944*a(n-4)+3429792*a(n-5)-38126443*a(n-6)+98209829*a(n-7)+162477726*a(n-8)-1059045499*a(n-9)+651177189*a(n-10)+3269771125*a(n-11)-4412158618*a(n-12)-3526224683*a(n-13)+7595898885*a(n-14)+727564626*a(n-15)-4875456557*a(n-16)+367654226*a(n-17)+1090025544*a(n-18)-17907882*a(n-19)-56592728*a(n-20)+3381324*a(n-21)+616392*a(n-22)-47520*a(n-23).

A184372 1/3 the number of (n+1)X6 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

58077, 15754461, 4210059673, 1127256514575, 301753233626727, 80778452206783159, 21624059735461675335, 5788675585887326994869, 1549605510397241533259837, 414823258633731476239250435

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 5 of A184376

			Some solutions for 3X6 with a(1,1)=0
..0..0..0..0..2..1....0..0..0..0..2..1....0..0..0..0..0..2....0..0..0..0..0..0
..2..0..0..0..1..1....2..0..0..0..0..0....0..0..0..1..0..0....2..0..0..1..0..2
..1..1..1..0..1..2....2..0..2..0..0..2....1..1..2..2..2..0....1..0..2..1..0..0

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

A184373 1/3 the number of (n+1)X7 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

420633, 281803871, 185547841629, 122443114867993, 80778452206783159, 53293289955084658949, 35159890626610196979641, 23196517518911246631354055, 15303755709562804997482560737, 10096556166552290137769922123373

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 6 of A184376

			Some solutions for 3X7 with a(1,1)=0
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..1..2..2..0..0..0..0....1..1..2..0..0..0..1....1..1..0..0..0..0..1
..1..1..2..0..2..0..0....0..0..2..0..2..0..0....0..1..0..1..0..2..1

R. H. Hardin, Table of n, a(n) for n = 1..154

A184374 1/3 the number of (n+1)X8 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

3046491, 5040682279, 8177524177277, 13299774554091575, 21624059735461675335, 35159890626610196979641, 57168347029530545962203193, 92953139774330929595592449437, 151137575901032303453595440035363

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 7 of A184376

			Some solutions for 3X8 with a(1,1)=0
..0..0..0..0..1..1..2..1....0..0..0..0..0..0..1..0....0..0..0..0..2..0..2..1
..0..0..0..0..0..1..2..0....0..0..0..0..2..2..2..0....0..0..0..0..1..1..1..1
..0..0..0..0..0..0..0..0....0..0..0..0..2..0..1..1....0..0..0..0..0..0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..84

A184375 1/3 the number of (n+1)X9 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

22064643, 90163722073, 360402692568245, 1444622701339019869, 5788675585887326994869, 23196517518911246631354055, 92953139774330929595592449437, 372482322079037724494019844619359

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Column 8 of A184376

			Some solutions for 3X9 with a(1,1)=0
..0..0..0..0..0..1..2..2..2....0..0..0..0..0..0..0..0..2
..0..0..0..0..0..0..2..2..2....0..0..0..0..0..2..1..0..1
..0..0..0..0..0..1..2..2..0....0..0..0..0..0..1..1..0..2

R. H. Hardin, Table of n, a(n) for n = 1..25

A184367 1/3 the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

Original entry on oeis.org

21, 2755, 2167173, 10378244309, 301753233626727, 53293289955084658949, 57168347029530545962203193, 372482322079037724494019844619359

Offset: 1

R. H. Hardin Jan 12 2011

nonn

Diagonal of A184376

			Some solutions for 3X3 with a(1,1)=0
..0..1..2....0..2..1....0..0..2....0..0..2....0..0..1....0..2..1....0..1..0
..2..1..1....1..1..1....2..2..2....0..0..2....2..0..2....0..0..1....0..1..2
..1..1..2....0..1..1....0..1..0....1..1..2....2..0..0....0..2..1....2..1..1

cp's OEIS Frontend

A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

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A184369 1/3 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

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A184370 1/3 the number of (n+1)X4 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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A184371 1/3 the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

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A184372 1/3 the number of (n+1)X6 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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A184373 1/3 the number of (n+1)X7 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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A184374 1/3 the number of (n+1)X8 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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A184375 1/3 the number of (n+1)X9 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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A184367 1/3 the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically.

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