A231855 -id:A231855 - cp's OEIS frontend

A231851 Number of nX4 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

8, 144, 7339, 360966, 17726611, 870478586, 42745416641, 2099041399895, 103074789422478, 5061554394805698, 248550911791818706, 12205253749015192168, 599346902427518296059, 29431318417158665841585

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Column 4 of A231855

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

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

Empirical: a(n) = 62*a(n-1) -697*a(n-2) +3287*a(n-3) -7718*a(n-4) +9336*a(n-5) -5629*a(n-6) +1612*a(n-7) -184*a(n-8) +4*a(n-9) for n>10

A231849 Number of n X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

1, 8, 656, 360966, 1454768048, 40798265169064, 8071247819035667716, 11185076987915709283036466, 108785685563255533314439981136006, 7419232013005838043632372688640525508734

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Diagonal of A231855

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

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

A231850 Number of n X 3 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

3, 34, 656, 12404, 234336, 4426924, 83630516, 1579892344, 29846280396, 563836173564, 10651619780176, 201223350436284, 3801378343993156, 71813123491132504, 1356645994919661436, 25628858153744306924

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

			Some solutions for n=5:
..0..0..1....0..0..1....0..0..1....0..0..2....0..0..2....0..0..0....0..0..0
..0..2..2....0..1..2....0..1..2....0..2..1....0..2..2....1..1..0....1..2..2
..0..2..2....0..2..0....0..2..1....0..1..1....2..0..1....0..2..2....0..2..2
..0..1..2....2..0..1....2..0..1....2..0..2....1..1..0....1..0..0....2..0..1
..0..0..1....1..2..2....2..2..2....2..2..0....1..0..0....1..0..0....0..2..2

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

Column 3 of A231855.

Empirical: a(n) = 21*a(n-1) - 41*a(n-2) + 22*a(n-3) for n>4.

Empirical g.f.: x*(3 - 29*x + 65*x^2 - 44*x^3) / (1 - 21*x + 41*x^2 - 22*x^3). - Colin Barker, Oct 01 2018

A231852 Number of nX5 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

21, 612, 85288, 11149456, 1454768048, 189801034186, 24762957054535, 3230773305296573, 421512520908365354, 54993894395631067868, 7174943262940390093175, 936100477964636376119044

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Column 5 of A231855

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

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

Empirical: a(n) = 183*a(n-1) -8008*a(n-2) +164477*a(n-3) -1911762*a(n-4) +13545983*a(n-5) -59779265*a(n-6) +159414566*a(n-7) -218855372*a(n-8) +7532104*a(n-9) +451112826*a(n-10) -590711864*a(n-11) +106059884*a(n-12) +386076754*a(n-13) -374591713*a(n-14) +131217119*a(n-15) +37977619*a(n-16) -86897128*a(n-17) +54663372*a(n-18) -17127366*a(n-19) +3057852*a(n-20) -413220*a(n-21) for n>22

A231853 Number of nX6 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

55, 2613, 991167, 342945563, 118292347982, 40798265169064, 14071005227913420, 4852980371902817445, 1673755248583159267298, 577265190724597150269824, 199094282646348652645556638, 68666072406587433832844219579

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Column 6 of A231855

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 52

Empirical recurrence of order 52 (see link above)

A231854 Number of nX7 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

144, 11159, 11529929, 10582191628, 9669634711179, 8834385550338284, 8071247819035667716, 7374031793933846572072, 6737043309310397086712007, 6155079609468787512765196641, 5623387483230350498450778517294

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Column 7 of A231855

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

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

A231856 Number of 2 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

3, 8, 34, 144, 612, 2613, 11159, 47675, 203696, 870316, 3718550, 15888022, 67883780, 290042861, 1239248291, 5294859950, 22623022401, 96659996189, 412993219856, 1764570725956, 7539372796546, 32213014377497, 137634565007885

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

			Some solutions for n=7:
..0..0..0..2..2..2..2....0..2..2..2..2..0..2....0..2..2..1..1..2..2
..1..1..2..2..2..0..1....2..2..2..2..1..1..1....1..1..1..1..0..0..0

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

Row 2 of A231855.

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 5*a(n-3) - a(n-4) + 10*a(n-5) - 3*a(n-6) - 3*a(n-7) + a(n-8) for n>9.

Empirical g.f.: x*(3 - 7*x + 5*x^3 + 3*x^4 - 11*x^5 + x^6 + 3*x^7 - x^8) / ((1 + x - x^3)*(1 - 6*x + 8*x^2 - 2*x^3 - 3*x^4 + x^5)). - Colin Barker, Oct 01 2018

A231857 Number of 3Xn 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

9, 55, 656, 7339, 85288, 991167, 11529929, 134163686, 1561220559, 18167587282, 211412670503, 2460168784055, 28628514590530, 333144562652494, 3876739724171184, 45112880641621747, 524969986286019848

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Row 3 of A231855

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

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

Empirical: a(n) = 15*a(n-1) -33*a(n-2) -96*a(n-3) +258*a(n-4) +412*a(n-5) -873*a(n-6) -1455*a(n-7) +1110*a(n-8) +4203*a(n-9) +2658*a(n-10) -10249*a(n-11) -12826*a(n-12) +15687*a(n-13) +27224*a(n-14) -12857*a(n-15) -37317*a(n-16) +9206*a(n-17) +17841*a(n-18) +107*a(n-19) +3350*a(n-20) -8989*a(n-21) +583*a(n-22) +8*a(n-23) +12093*a(n-24) -21445*a(n-25) +13211*a(n-26) -2506*a(n-27) +2401*a(n-28) -2357*a(n-29) +397*a(n-30) -8*a(n-31) +70*a(n-32) -32*a(n-33) -10*a(n-34) -4*a(n-35) for n>39

A231858 Number of 4Xn 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

27, 377, 12404, 360966, 11149456, 342945563, 10582191628, 326538750032, 10077070157886, 310990560701053, 9597588422538259, 296194800363244561, 9140981229461743667, 282103332885578653809, 8706099363813295026694

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Row 4 of A231855

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

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

A231859 Number of 5 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Original entry on oeis.org

81, 2584, 234336, 17726611, 1454768048, 118292347982, 9669634711179, 790105900385455, 64578303092773705, 5278241081510497850, 431415634830501378047, 35261742427088235238529, 2882118653532747073628155

Offset: 1

R. H. Hardin, Nov 14 2013

nonn

Row 5 of A231855.

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

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

Cf. A231855.

cp's OEIS Frontend

A231851 Number of nX4 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

Formula

A231849 Number of n X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

A231850 Number of n X 3 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A231852 Number of nX5 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

Formula

A231853 Number of nX6 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

Formula

A231854 Number of nX7 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

A231856 Number of 2 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A231857 Number of 3Xn 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

Formula

A231858 Number of 4Xn 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

A231859 Number of 5 X n 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs