A230661 -id:A230661 - cp's OEIS frontend

A230658 Number of nX3 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

0, 3, 15, 21, 135, 177, 1155, 1509, 9855, 12873, 84075, 109821, 717255, 936897, 6118995, 7992789, 52201935, 68187513, 445341435, 581716461, 3799265175, 4962698097, 32412020835, 42337417029, 276511126815, 361185960873

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 3 of A230661

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

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

Empirical: a(n) = 9*a(n-2) -4*a(n-4).

Empirical: G.f. -3*x^2*(-1-5*x+2*x^2) / ( 1-9*x^2+4*x^4 ). - R. J. Mathar, Oct 27 2013

A230659 Number of n X 5 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 15, 135, 531, 8613, 28161, 477279, 1539207, 26178201, 84335553, 1434726783, 4621740687, 78627215025, 253283346081, 4308981442911, 13880597644287, 236143613924865, 760693546670625, 12941296146524511, 41688023124390687

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

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

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

Column 5 of A230661.

Empirical: a(n) = 59*a(n-2) - 230*a(n-4) - 2*a(n-6) + 32*a(n-8) for n>10.

Empirical g.f.: 3*x^2*(5 + 45*x - 118*x^2 + 216*x^3 + 94*x^4 + 54*x^5 - 44*x^6 - 16*x^8) / (1 - 59*x^2 + 230*x^4 + 2*x^6 - 32*x^8). - Colin Barker, Sep 22 2018

A230660 Number of nX7 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 63, 1155, 11745, 477279, 3951657, 169006665, 1374288243, 59075291211, 479621050353, 20625942501183, 167435671598913, 7200781142959245, 58453268091967479, 2513864130034802115, 20406595554618417837

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Column 7 of A230661

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

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

Empirical: a(n) = 390*a(n-2) -14687*a(n-4) +146138*a(n-6) -823339*a(n-8) -2774563*a(n-10) +26807114*a(n-12) -60400888*a(n-14) +106367378*a(n-16) -35490451*a(n-18) -7548040169*a(n-20) +1542760687*a(n-22) +7961883650*a(n-24) +3473400076*a(n-26) +61902164677*a(n-28) +25546220017*a(n-30) +84369583536*a(n-32) +75320917456*a(n-34) +42723111397*a(n-36) -5387877662*a(n-38) +926204972*a(n-40) -121037200*a(n-42) +10124352*a(n-44) +414720*a(n-46) for n>47

A230657 Number of n X n 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

1, 3, 15, 123, 8613, 337977, 169006665, 40860127671, 131515599970167, 201844710508818147, 4141132208926170478473, 40464088148356899296269059

Offset: 1

R. H. Hardin, Oct 27 2013

nonn

Diagonal of A230661

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

cp's OEIS Frontend

A230658 Number of nX3 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

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A230659 Number of n X 5 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

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A230660 Number of nX7 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

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A230657 Number of n X n 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

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