A197450 -id:A197450 - cp's OEIS frontend

A197444 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

2, 5, 12, 36, 107, 321, 957, 2868, 8581, 25694, 76914, 230273, 689377, 2063867, 6178778, 18498023, 55379290, 165794354, 496354537, 1485984549, 4448735449, 13318609060, 39873206463, 119372269782, 357376295102, 1069911935955

Offset: 1

R. H. Hardin, Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's.

Column 2 of A197450.

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

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

Cf. A197450.

Empirical: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -6*a(n-4) -a(n-5) +4*a(n-7) +a(n-8).

Empirical g.f.: x*(2 + x - 8*x^2 - 5*x^3 + 7*x^4 + 7*x^5 + x^6 - 3*x^7) / ((1 - x)*(1 - x - 6*x^2 - 2*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + x^7)). - Colin Barker, May 12 2018

A197445 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

3, 12, 81, 474, 2678, 15410, 88767, 510482, 2936714, 16895217, 97197637, 559175541, 3216923150, 18506887013, 106469709385, 612517802024, 3523801014059, 20272347435052, 116626354899557, 670948774602366, 3859953085161367

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Column 3 of A197450

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

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

Empirical: a(n) = 2*a(n-1) +12*a(n-2) +45*a(n-3) +61*a(n-4) +20*a(n-5) -129*a(n-6) -324*a(n-7) -344*a(n-8) -166*a(n-9) +61*a(n-10) +268*a(n-11) +360*a(n-12) +307*a(n-13) +240*a(n-14) +92*a(n-15) -97*a(n-16) -142*a(n-17) -120*a(n-18) -92*a(n-19) -32*a(n-20) -4*a(n-22) for n>25

A197446 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

4, 36, 474, 4837, 52117, 585194, 6455759, 71202438, 787298158, 8700460833, 96129107870, 1062244177133, 11737953179188, 129703872646573, 1433228960340464, 15837211757913841, 175001375414696401

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Column 4 of A197450

			Some solutions containing all values 0 to 4 for n=5
..0..1..1..2....0..0..1..1....0..3..0..0....0..0..0..0....0..0..0..0
..3..0..0..1....0..4..0..0....3..0..4..0....3..0..4..0....0..4..0..0
..0..0..0..1....3..0..3..0....0..0..0..1....0..0..0..1....0..0..3..0
..0..4..0..0....0..1..2..1....0..3..0..1....0..3..0..1....0..1..2..1
..0..0..3..0....0..1..2..1....0..1..1..2....0..1..1..2....0..1..2..1

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

Empirical: a(n) = 5*a(n-1) +43*a(n-2) +266*a(n-3) +239*a(n-4) -1960*a(n-5) -10352*a(n-6) -9192*a(n-7) +37799*a(n-8) +105029*a(n-9) -18744*a(n-10) -238355*a(n-11) -126539*a(n-12) +355537*a(n-13) +283213*a(n-14) -719109*a(n-15) -385554*a(n-16) +828862*a(n-17) +1313412*a(n-18) -2023532*a(n-19) -2243258*a(n-20) +1255883*a(n-21) +1718260*a(n-22) -1386751*a(n-23) -2333466*a(n-24) +1949938*a(n-25) +3566040*a(n-26) -4067978*a(n-27) -123658*a(n-28) +2185717*a(n-29) +1568417*a(n-30) -1624352*a(n-31) -2532073*a(n-32) +4246890*a(n-33) -1297116*a(n-34) -1336520*a(n-35) +1883451*a(n-36) -1106741*a(n-37) +813615*a(n-38) -847011*a(n-39) -13406*a(n-40) +890240*a(n-41) -936883*a(n-42) +427611*a(n-43) +113100*a(n-44) -369138*a(n-45) +191138*a(n-46) +24776*a(n-47) -53551*a(n-48) +9522*a(n-49) +1877*a(n-50) +85*a(n-51) -54*a(n-52) +36*a(n-53) for n>56

A197447 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

7, 107, 2678, 52117, 1108699, 23829080, 504568165, 10724642167, 228248265080, 4853181015432, 103200753393047, 2194748772730124, 46673287485335449, 992547357156970890, 21107504726738892508, 448871249985110511395

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Column 5 of A197450

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

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

A197448 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

11, 321, 15410, 585194, 23829080, 982926107, 40087361395, 1640477445822, 67160665746869, 2747685400705119, 112433629005651948, 4600917175526994358, 188267595598497672073, 7703877269427034462338, 315242428170240015474340

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Column 6 of A197450

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

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

A197449 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

16, 957, 88767, 6455759, 504568165, 40087361395, 3148323076125, 247785141871837, 19514460176530843, 1536223846055481075, 120945067934443941208, 9522042330180130196817, 749659600975504964938552

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Column 7 of A197450

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

R. H. Hardin, Table of n, a(n) for n = 1..158

A197443 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 5, 81, 4837, 1108699, 982926107, 3148323076125, 37516007592943532, 1657994465210882573048

Offset: 1

R. H. Hardin Oct 15 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's

Diagonal of A197450

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

cp's OEIS Frontend

A197444 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197445 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197446 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197447 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197448 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197449 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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A197443 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

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