A262420 -id:A262420 - cp's OEIS frontend

A262414 Number of (n+1) X (2+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

0, 4, 12, 48, 144, 468, 1404, 4320, 12960, 39204, 117612, 353808, 1061424, 3187188, 9561564, 28693440, 86080320, 258267204, 774801612, 2324483568, 6973450704, 20920588308, 62761764924, 188286003360, 564858010080, 1694576156004

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

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

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

Column 2 of A262420.

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3).

Empirical g.f.: 4*x^2 / ((1 - 3*x)*(1 - 3*x^2)). - Colin Barker, Dec 31 2018

A262415 Number of (n+1) X (3+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

6, 45, 270, 1701, 10206, 61965, 371790, 2237301, 13423806, 80601885, 483611310, 2902199301, 17413195806, 104483957805, 626903746830, 3761465527701, 22568793166206, 135413146417725, 812478878506350, 4874876757822501

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

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

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

Column 3 of A262420.

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 + 3*x - 18*x^2) /  ((1 - 3*x)*(1 + 3*x)*(1 - 6*x)).
a(n) = 3^(n-1) * (2^(n+3) - 2) / 2 for n even.
a(n) = 3^(n-1) * (2^(n+3) - 4) / 2 for n odd.
(End)

A262416 Number of (n+1) X (4+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

0, 114, 1260, 18228, 200880, 2353338, 25901100, 289462380, 3184570800, 35172555474, 386913644460, 4260476333988, 46865727906480, 515660423584938, 5672279881478700, 62399341247906460, 686393226739623600

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

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

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

Column 4 of A262420.

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.: 6*x^2*(19 + x - 184*x^2 + 14*x^3) / ((1 - 2*x)*(1 + 2*x)*(1 - 11*x)*(1 - 13*x^2)*(1 - 31*x^2)). - Colin Barker, Dec 31 2018

A262417 Number of (n+1)X(5+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

22, 709, 15310, 428301, 9401742, 220808869, 4856629870, 108673357501, 2390753728462, 52824430238229, 1162134451107630, 25594859555510701, 563086760980631182, 12391301216924710789, 272608619423065220590

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Column 5 of A262420.

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

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

Cf. A262420.

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)

A262418 Number of (n+1)X(6+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

0, 2892, 124572, 7577424, 326005344, 15231780324, 655089996204, 28755516792360, 1236553617638640, 53446495303862172, 2298231625018170492, 98951519822732397504, 4254930564828132559104, 183021121626516730866324

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Column 6 of A262420.

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

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

Cf. A262420.

Empirical: a(n) = 43*a(n-1) +777*a(n-2) -33411*a(n-3) -179235*a(n-4) +7707105*a(n-5) +17148167*a(n-6) -737371181*a(n-7) -706190268*a(n-8) +30366181524*a(n-9) +11010302352*a(n-10) -473443001136*a(n-11) -33794555200*a(n-12) +1453165873600*a(n-13)

A262419 Number of (n+1)X(7+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

86, 15293, 1299070, 163388421, 14036526126, 1326209720893, 114043973318270, 10040316574125941, 863461131233308366, 74693845931156134893, 6423667242365667891870, 553245019071999716394661

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Column 7 of A262420.

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

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

Cf. A262420.

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)

A262421 Number of (2+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

5, 4, 45, 114, 709, 2892, 15293, 72370, 367125, 1808844, 9078925, 45214674, 226307429, 1130307532, 5653140573, 28257215730, 141297157045, 706426855884, 3532211260205, 17660645718034, 88303765183749, 441515959527372

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

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

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

Row 2 of A262420.

Empirical: a(n) = 5*a(n-1) + 12*a(n-2) - 60*a(n-3) - 39*a(n-4) + 195*a(n-5) + 28*a(n-6) - 140*a(n-7).

Empirical g.f.: x*(5 - 21*x - 35*x^2 + 141*x^3 + 34*x^4 - 140*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 5*x)*(1 - 7*x^2)). - Colin Barker, Dec 31 2018

A262422 Number of (3+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

10, 12, 270, 1260, 15310, 124572, 1299070, 12380940, 124921710, 1235566332, 12379963870, 123483616620, 1235387708110, 12346379507292, 123476688644670, 1234585890852300, 12346166930494510, 123457247499499452

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Row 3 of A262420.

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

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

Cf. A262420.

Empirical: a(n) = 10*a(n-1) +46*a(n-2) -460*a(n-3) -609*a(n-4) +6090*a(n-5) +2164*a(n-6) -21640*a(n-7) -1600*a(n-8) +16000*a(n-9).

A262423 Number of (4+1)X(n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

21, 48, 1701, 18228, 428301, 7577424, 163388421, 3287265300, 69481709901, 1443547193328, 30363542104581, 635919555126708, 13359727300650381, 280364385485387664, 5888252348126720901, 123632237885054793300

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Row 4 of A262420.

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

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

Cf. A262420.

Empirical: a(n) = 21*a(n-1) +189*a(n-2) -3969*a(n-3) -10719*a(n-4) +225099*a(n-5) +250803*a(n-6) -5266863*a(n-7) -2527200*a(n-8) +53071200*a(n-9) +9062928*a(n-10) -190321488*a(n-11)

A262424 Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

42, 144, 10206, 200880, 9401742, 326005344, 14036526126, 562188062160, 23753751161742, 985963486014144, 41471657300369646, 1736701374341409840, 72968249610859102542, 3062420548152290816544, 128633450602627230830766

Offset: 1

R. H. Hardin, Sep 22 2015

nonn

Row 5 of A262420.

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

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

Cf. A262420.

Empirical: a(n) = 42*a(n-1) +711*a(n-2) -29862*a(n-3) -141183*a(n-4) +5929686*a(n-5) +10349613*a(n-6) -434683746*a(n-7) -267400116*a(n-8) +11230804872*a(n-9) +1666598976*a(n-10) -69997156992*a(n-11)

cp's OEIS Frontend

A262414 Number of (n+1) X (2+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262415 Number of (n+1) X (3+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262416 Number of (n+1) X (4+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262417 Number of (n+1)X(5+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262418 Number of (n+1)X(6+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262419 Number of (n+1)X(7+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262421 Number of (2+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262422 Number of (3+1) X (n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262423 Number of (4+1)X(n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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A262424 Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

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