A221035 -id:A221035 - cp's OEIS frontend

A221030 Majority value maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

4, 33, 228, 1561, 10648, 72625, 495329, 3378333, 23041525, 157152036, 1071837150, 7310340394, 49859324875, 340059715828, 2319337668908, 15818772327435, 107890093495975, 735851811608802, 5018791541488065, 34230082931837488

Offset: 1

R. H. Hardin, Dec 29 2012

nonn

Column 3 of A221035.

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

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

Cf. A221035.

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

Empirical g.f.: x*(4 + x - 4*x^2 + 5*x^3 - 3*x^4) / (1 - 8*x + 8*x^2 + x^3 - 5*x^4 + 2*x^5). - Colin Barker, Mar 13 2018

A221031 Majority value maps: number of n X 4 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X 4 array.

Original entry on oeis.org

7, 119, 1733, 24485, 345755, 4882030, 68933905, 973340015, 13743460075, 194056216948, 2740053437074, 38689267213364, 546288396106862, 7713534869291859, 108914303513829210, 1537858544870732685

Offset: 1

R. H. Hardin, Dec 29 2012

nonn

Column 4 of A221035.

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

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

Cf. A221035.

Empirical: a(n) = 22*a(n-1) -139*a(n-2) +446*a(n-3) -825*a(n-4) +817*a(n-5) -168*a(n-6) -528*a(n-7) +480*a(n-8) +48*a(n-9) -208*a(n-10) +64*a(n-11) for n>12.

A221036 Majority value maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 2 X n array.

Original entry on oeis.org

1, 7, 33, 119, 457, 1710, 6466, 24433, 92196, 347977, 1313608, 4958107, 18714962, 70641589, 266642543, 1006466983, 3799003546, 14339684590, 54126460553, 204305303067, 771169136489, 2910848804238, 10987266400303, 41472446978323

Offset: 1

R. H. Hardin, Dec 29 2012

nonn

Row 2 of A221035.

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

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

Cf. A221035.

Empirical: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) -12*a(n-4) -2*a(n-5) +22*a(n-6) -20*a(n-7) +16*a(n-8) +8*a(n-9) -6*a(n-10) -10*a(n-11) +a(n-12) +2*a(n-13) -2*a(n-14) +2*a(n-15) for n>19.

A221032 Majority value maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

Original entry on oeis.org

12, 457, 14277, 419506, 12239631, 356411031, 10373626389, 301896920812, 8785647712335, 255673459067107, 7440407252788968, 216524761820591729, 6301129172106645040, 183370379451163145156, 5336296861965965103306

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Column 5 of A221035

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

R. H. Hardin, Table of n, a(n) for n = 1..104

Empirical: a(n) = 68*a(n-1) -1822*a(n-2) +27547*a(n-3) -272852*a(n-4) +1918678*a(n-5) -10038025*a(n-6) +40128709*a(n-7) -124183787*a(n-8) +298025391*a(n-9) -548633708*a(n-10) +750796914*a(n-11) -705582380*a(n-12) +354260143*a(n-13) +14095215*a(n-14) +79575304*a(n-15) -761514246*a(n-16) +1481099928*a(n-17) -1471900372*a(n-18) +606133206*a(n-19) +406829334*a(n-20) -787855272*a(n-21) +480146240*a(n-22) -35768060*a(n-23) -108927108*a(n-24) +442396*a(n-25) +104024712*a(n-26) -98101144*a(n-27) +46460464*a(n-28) -15969760*a(n-29) +8560160*a(n-30) -5517056*a(n-31) +2030976*a(n-32) -268288*a(n-33) -29696*a(n-34) +8192*a(n-35) for n>41

A221033 Majority value maps: number of nX6 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX6 array.

Original entry on oeis.org

21, 1710, 110506, 6637755, 393788081, 23287585899, 1376083439034, 81296621316610, 4802591348249077, 283708464262466290, 16759739541027933054, 990060650898808032184, 58486579373224774257276, 3455020389521403479154432

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Column 6 of A221035

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

R. H. Hardin, Table of n, a(n) for n = 1..68

A221034 Majority value maps: number of nX7 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX7 array.

Original entry on oeis.org

37, 6466, 870027, 106761517, 12843452050, 1537391091350, 183738465400508, 21948812185231460, 2621564010810005248, 313106029844989170530, 37395287501846784190818, 4466225820942761145748924

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Column 7 of A221035

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

R. H. Hardin, Table of n, a(n) for n = 1..43

A221037 Majority value maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

Original entry on oeis.org

1, 21, 228, 1733, 14277, 110506, 870027, 6717882, 52248430, 404872294, 3137029417, 24306328888, 188293396538, 1458607561162, 11298886140485, 87523428512115, 677973532822056, 5251692364017630, 40680417109724197, 315116602409454269

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Row 3 of A221035

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

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

A221038 Majority value maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

Original entry on oeis.org

1, 65, 1561, 24485, 419506, 6637755, 106761517, 1679728622, 26519446624, 415662734974, 6527075798544, 102305652745928, 1603242301015531, 25121020499653935, 393548527029714107, 6165086304179204952

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Row 4 of A221035

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

R. H. Hardin, Table of n, a(n) for n = 1..26

A221029 Majority value maps: number of n X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X n array.

Original entry on oeis.org

1, 7, 228, 24485, 12239631, 23287585899, 183738465400508

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Diagonal of A221035

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

A221039 Majority value maps: number of 5Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 5Xn array.

Original entry on oeis.org

1, 200, 10648, 345755, 12239631, 393788081, 12843452050, 407831788165

Offset: 1

R. H. Hardin Dec 29 2012

nonn

Row 5 of A221035

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

cp's OEIS Frontend

A221030 Majority value maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A221031 Majority value maps: number of n X 4 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X 4 array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A221036 Majority value maps: number of 2 X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 2 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A221032 Majority value maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

Views

Author

Keywords

Comments

Examples

Links

Formula

A221033 Majority value maps: number of nX6 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX6 array.

Views

Author

Keywords

Comments

Examples

Links

A221034 Majority value maps: number of nX7 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 nX7 array.

Views

Author

Keywords

Comments

Examples

Links

A221037 Majority value maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

Views

Author

Keywords

Comments

Examples

Links

A221038 Majority value maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

Views

Author

Keywords

Comments

Examples

Links

A221029 Majority value maps: number of n X n binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 n X n array.

Views

Author

Keywords

Comments

Examples

A221039 Majority value maps: number of 5Xn binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..2 5Xn array.

Views

Author

Keywords

Comments

Examples