A262917 -id:A262917 - cp's OEIS frontend

A262920 Number of (6+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

19, 61, 1207, 7417, 152587, 1550557, 30497815, 420921961, 7895204299, 126160746301, 2313326012887, 39531526974937, 720265713036427, 12724622932131997, 232102910290030615, 4177632885527495881

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Row 6 of A262917.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 65

Cf. A262917.

Empirical recurrence of order 65 (see link above)

A262912 Number of (n+1)X(3+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 6, 15, 53, 318, 1207, 5797, 34782, 189135, 1089701, 6538206, 38547751, 229660021, 1377960126, 8242589055, 49395098933, 296370593598, 1777250964247, 10661181588037, 63967089528222, 383764138693935, 2302493636842181

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Column 3 of A262917.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of empirical formula for A262912

Cf. A262917.

Empirical: a(n) = 8*a(n-1) -16*a(n-2) +104*a(n-3) -640*a(n-4) +1280*a(n-5) -3830*a(n-6) +15280*a(n-7) -30560*a(n-8) +58240*a(n-9) -99200*a(n-10) +198400*a(n-11) -283209*a(n-12) -115128*a(n-13) +230256*a(n-14) -345384*a(n-15).

Empirical formula verified: see link. - Robert Israel, Aug 12 2019

A262913 Number of (n+1)X(4+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 11, 33, 137, 1411, 7417, 51769, 529931, 4701201, 44632313, 454922851, 4573641865, 46374477961, 476430252011, 4902011719233, 50649718388009, 526357874613571, 5483464232074777, 57393678601087705, 603752064813378251

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Column 4 of A262917.

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

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

Cf. A262917.

A262914 Number of (n+1)X(5+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 22, 99, 853, 18190, 152587, 2045269, 42299374, 727767387, 13958567845, 286835405806, 5764350599731, 117817168320181, 2437382604831502, 50489841095677539, 1050381458044863253, 21936143744564786830

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Column 5 of A262917.

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

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

Cf. A262917.

A262918 Number of (4+1) X (n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

5, 9, 53, 137, 853, 2953, 17333, 71721, 394325, 1791209, 9435253, 44924617, 230950613, 1126125513, 5713545653, 28200027881, 142082597845, 705663892009, 3542422689653, 17650591452297, 88436516562773, 441384307595273

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

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

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

Row 4 of A262917.

Empirical: a(n) = 7*a(n-1) + 11*a(n-2) - 147*a(n-3) + 99*a(n-4) + 777*a(n-5) - 1019*a(n-6) - 637*a(n-7) + 910*a(n-8).

Empirical g.f.: x*(5 - 26*x - 65*x^2 + 402*x^3 + 139*x^4 - 1510*x^5 + 273*x^6 + 910*x^7) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 5*x)*(1 - 7*x^2)*(1 - 13*x^2)). - Colin Barker, Jan 01 2019

A262919 Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

10, 27, 318, 1411, 18190, 121507, 1444558, 12031011, 132033870, 1214394787, 12726094798, 122360994211, 1252258147150, 12289486776867, 124300598233038, 1231754978783011, 12386462076574030, 123317516595907747

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Row 5 of A262917.

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

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

Cf. A262917.

Empirical: a(n) = 14*a(n-1) +39*a(n-2) -1106*a(n-3) +1561*a(n-4) +22386*a(n-5) -57539*a(n-6) -89894*a(n-7) +251940*a(n-8) +68600*a(n-9) -196000*a(n-10)

A262921 Number of (7+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

37, 145, 5797, 51769, 2045269, 33948145, 1282949605, 32134185721, 1167936430357, 36073199081665, 1296185238921637, 44004551333065849, 1586887190270675029, 56226197936849068945, 2042436589392526147045, 73857813970541521390201

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Row 7 of A262917.

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

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

Cf. A262917.

A262911 Number of (n+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 3, 15, 137, 18190, 1550557, 1282949605

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Diagonal of A262917.

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

Cf. A262917.

A262915 Number of (n+1)X(6+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 43, 261, 2953, 121507, 1550557, 33948145, 1361585275, 42115306149, 1516528236361, 61572663026659, 2451674386383133, 100125715548126961

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Column 6 of A262917.

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

Cf. A262917.

A262916 Number of (n+1)X(7+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

1, 86, 783, 17333, 1444558, 30497815, 1282949605, 102437680622

Offset: 1

R. H. Hardin, Oct 04 2015

nonn

Column 7 of A262917.

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

Cf. A262917.

cp's OEIS Frontend

A262920 Number of (6+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262912 Number of (n+1)X(3+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262913 Number of (n+1)X(4+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262914 Number of (n+1)X(5+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262918 Number of (4+1) X (n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262919 Number of (5+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262921 Number of (7+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262911 Number of (n+1)X(n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262915 Number of (n+1)X(6+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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A262916 Number of (n+1)X(7+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

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