A262332 -id:A262332 - cp's OEIS frontend

A262326 Number of (n+1) X (2+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

3, 5, 15, 33, 99, 261, 783, 2241, 6723, 19845, 59535, 177633, 532899, 1595781, 4787343, 14353281, 43059843, 129153285, 387459855, 1162300833, 3486902499, 10460471301, 31381413903, 94143533121, 282430599363, 847289672325

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

Column 2 of A262332.

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

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

Cf. A262332.

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3).
Conjectures from Colin Barker, Mar 20 2018: (Start)
G.f.: x*(3 - 4*x - 9*x^2) / ((1 - 3*x)*(1 - 3*x^2)).
a(n) = 2*3^(n/2-1) + 3^(n-1) for n even.
a(n) = 2*3^((n-3)/2+1) + 3^(n-1) for n odd.
(End)

A262325 Number of (n+1)X(n+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

2, 5, 90, 2399, 570922, 394241389, 1456404454010, 19392931688071671, 1134083007177482717802, 256890679674803015904974405, 239672757231397671662393429466490

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

Diagonal of A262332.

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

R. H. Hardin, Table of n, a(n) for n = 1..12

Cf. A262332.

A262327 Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

6, 15, 90, 351, 2106, 10935, 65610, 378351, 2270106, 13482855, 80897130, 484142751, 2904856506, 17417978775, 104507872650, 626946793551, 3761680761306, 22569180586695, 135415083520170, 812482365290751, 4874894191744506

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

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

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

Column 3 of A262332.

Empirical: a(n) = 6*a(n-1) + 9*a(n-2) - 54*a(n-3).
Conjectures from Colin Barker, Dec 31 2018: (Start)
G.f.: 3*x*(2 - 7*x - 18*x^2) / ((1 - 3*x)*(1 + 3*x)*(1 - 6*x)).
a(n) = 3^(n-2)*(14 + 2^(2+n)) / 2 for n even.
a(n) = 3^(n-2)*(28 + 2^(2+n)) / 2 for n odd.
(End)

A262328 Number of (n+1) X (4+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

11, 33, 351, 2399, 26131, 252097, 2767631, 29452071, 323841891, 3532758473, 38856792031, 426525918799, 4691681673011, 51580839266577, 567386112244911, 6240392439847991, 68644221256999171, 755059969459250713

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

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

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

Column 4 of A262332.

Empirical: a(n) = 11*a(n-1) + 48*a(n-2) - 528*a(n-3) - 579*a(n-4) + 6369*a(n-5) + 1612*a(n-6) - 17732*a(n-7).

Empirical g.f.: x*(11 - 88*x - 540*x^2 + 2762*x^3 + 6687*x^4 - 16120*x^5 - 17732*x^6) / ((1 - 2*x)*(1 + 2*x)*(1 - 11*x)*(1 - 13*x^2)*(1 - 31*x^2)). - Colin Barker, Dec 31 2018

A262329 Number of (n+1)X(5+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

22, 99, 2106, 26131, 570922, 10789339, 237172426, 5028462531, 110616890922, 2411745951979, 53057962551946, 1164684632805331, 25623040149388522, 563395838251985019, 12394707380225550666, 272646042792758242531

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

Column 5 of A262332.

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

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

Cf. A262332.

Empirical: a(n) = 22*a(n-1) +215*a(n-2) -4730*a(n-3) -14143*a(n-4) +311146*a(n-5) +364285*a(n-6) -8014270*a(n-7) -3615956*a(n-8) +79551032*a(n-9) +9486400*a(n-10) -208700800*a(n-11)

A262330 Number of (n+1) X (6+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

43, 261, 10935, 252097, 10789339, 394241389, 16940254423, 699094613961, 30056993215803, 1279198648576981, 55003871225837815, 2359070696262035857, 101439297012081117979, 4359072407628680510589, 187439773845177573589143

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

Column 6 of A262332.

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

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

Cf. A262332.

Empirical: a(n) = 43*a(n-1) +793*a(n-2) -34099*a(n-3) -191667*a(n-4) +8241681*a(n-5) +20015927*a(n-6) -860684861*a(n-7) -980560940*a(n-8) +42164120420*a(n-9) +22309346640*a(n-10) -959301905520*a(n-11) -209959392832*a(n-12) +9028253891776*a(n-13) +540712883200*a(n-14) -23250653977600*a(n-15).

A262331 Number of (n+1)X(7+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

86, 783, 65610, 2767631, 237172426, 16940254423, 1456404454010, 119519290640511, 10278397804194666, 873639089311509863, 75132812815390491610, 6442513290262072850191, 554056059394660086575306

Offset: 1

R. H. Hardin, Sep 18 2015

nonn

Column 7 of A262332.

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

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

Cf. A262332.

Empirical: a(n) = 86*a(n-1) +3252*a(n-2) -279672*a(n-3) -3329646*a(n-4) +286349556*a(n-5) +1544583660*a(n-6) -132834194760*a(n-7) -365579378025*a(n-8) +31439826510150*a(n-9) +46337467429704*a(n-10) -3985022198954544*a(n-11) -3102790005466128*a(n-12) +266839940470087008*a(n-13) +99548995158787584*a(n-14) -8561213583655732224*a(n-15) -1170690303846912000*a(n-16) +100679366130834432000*a(n-17) +3277061542543360000*a(n-18) -281827292658728960000*a(n-19)

cp's OEIS Frontend

A262326 Number of (n+1) X (2+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262325 Number of (n+1)X(n+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262327 Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262328 Number of (n+1) X (4+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262329 Number of (n+1)X(5+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262330 Number of (n+1) X (6+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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A262331 Number of (n+1)X(7+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

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