cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A262844 Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

6, 34, 132, 396, 1264, 3962, 11886, 35914, 108556, 325668, 976552, 2931922, 8795766, 26370674, 79104084, 237312252, 711756448, 2135076202, 6405228606, 19214238554, 57640739420, 172922218260, 518757049560, 1556255741762, 4668767225286
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Column 2 of A262849.

Examples

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

Crossrefs

Cf. A262849.

Programs

  • Mathematica
    v = Select[Tuples[{0, 1}, 4], Mod[FromDigits[#, 2], 7] == 0 &];
    a[n_] := a[n] = Length[Select[Tuples[v, n + 2], !AnyTrue[Transpose[#], Mod[FromDigits[#, 2], 7] == 0 &] &]];
    Table[a[n], {n, 1, 10}] (* Robert P. P. McKone, Jun 09 2024 *)

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) -68*a(n-4) +68*a(n-5) -162*a(n-6) +444*a(n-7) -444*a(n-8) +644*a(n-9) -1244*a(n-10) +1244*a(n-11) -1277*a(n-12) +1376*a(n-13) -1376*a(n-14) +1032*a(n-15).

A262845 Number of (n+2)X(3+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

12, 196, 1336, 5184, 31512, 175820, 793812, 4140908, 21744992, 104726376, 525986400, 2691397140, 13304013852, 66260714708, 334758471368, 1670112463824, 8315216847336, 41755671803804, 208872540829092, 1041336962146684
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Column 3 of A262849.

Examples

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

Crossrefs

Cf. A262849.

Formula

Empirical: a(n) = 5*a(n-1) +203*a(n-3) -1015*a(n-4) -17262*a(n-6) +86310*a(n-7) +803306*a(n-9) -4016530*a(n-10) -22920723*a(n-12) +114603615*a(n-13) +424713065*a(n-15) -2123565325*a(n-16) -5289109868*a(n-18) +26445549340*a(n-19) +45727616604*a(n-21) -228638083020*a(n-22) -289788580823*a(n-24) +1448942904115*a(n-25) +1453125527917*a(n-27) -7265627639585*a(n-28) -5836364956590*a(n-30) +29181824782950*a(n-31) +16212555187738*a(n-33) -81062775938690*a(n-34) -21276199455861*a(n-36) +106380997279305*a(n-37) -6355957095425*a(n-39) +31779785477125*a(n-40) +38763541794536*a(n-42) -193817708972680*a(n-43)

A262846 Number of (n+2)X(4+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

318, 3181, 37635, 420654, 3896365, 39348387, 417279054, 3999504445, 39913429587, 409857534030, 4017392736541, 40104536998707, 405732145282158, 4021339824862381, 40178930760566115, 403823141865184494
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Column 4 of A262849.

Examples

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

Crossrefs

Cf. A262849.

Formula

Empirical: a(n) = 13*a(n-1) -30*a(n-2) +775*a(n-3) -10075*a(n-4) +23250*a(n-5) -187265*a(n-6) +2434445*a(n-7) -5617950*a(n-8) +18375455*a(n-9) -238880915*a(n-10) +551263650*a(n-11) -585288123*a(n-12) +7608745599*a(n-13) -17558643690*a(n-14) -12851058675*a(n-15) +167063762775*a(n-16) -385531760250*a(n-17) +757921180765*a(n-18) -9852975349945*a(n-19) +22737635422950*a(n-20) -1115961555955*a(n-21) +14507500227415*a(n-22) -33478846678650*a(n-23) -69403913471776*a(n-24) +902250875133088*a(n-25) -2082117404153280*a(n-26) -67517783528000*a(n-27) +877731185864000*a(n-28) -2025533505840000*a(n-29)

A262847 Number of (n+2)X(5+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

900, 31050, 771084, 14762016, 290338650, 5692555116, 108936025308, 2071613294466, 39520865526156, 752512142640600, 14283775460054754, 271538648699660460, 5162251935414132180, 98038344198110173098
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Column 5 of A262849.

Examples

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

Crossrefs

Cf. A262849.

A262850 Number of (1+2)X(n+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

6, 6, 12, 318, 900, 4536, 34782, 178926, 1042284, 6538206, 38160540, 227814120, 1377960126, 8227422006, 49321272972, 296370593598, 1776644188020, 10658199015576, 63967089528222, 383739633130686, 2302372435469484
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Row 1 of A262849.

Examples

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

Crossrefs

Cf. A262849.

Formula

Empirical: a(n) = 6*a(n-1) +72*a(n-3) -432*a(n-4) -1270*a(n-6) +7620*a(n-7) -2880*a(n-9) +17280*a(n-10) +113591*a(n-12) -681546*a(n-13) +115128*a(n-15) -690768*a(n-16)

A262851 Number of (2+2)X(n+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

13, 34, 196, 3181, 31050, 352880, 4679725, 58693450, 749598500, 9769811821, 126477115922, 1640601801744, 21334300812253, 277222463778754, 3602979823609668, 46840315814579821, 608897998235183514
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Row 2 of A262849.

Examples

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

Crossrefs

Cf. A262849.

A262852 Number of (3+2)X(n+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

27, 132, 1336, 37635, 771084, 17912392, 481968171, 12572589132, 333224229896, 8994193541379, 241857613967412, 6515666351143848, 175918432063803627, 4747650731553770292, 128153708240382030872, 3460143599773663664643
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Row 3 of A262849.

Examples

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

Crossrefs

Cf. A262849.

A262853 Number of (4+2)X(n+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

54, 396, 5184, 420654, 14762016, 661066920, 35819485902, 1848763876932, 97674093333720, 5273363053187598, 283250082728896200, 15255186777350855280, 823762481842229569614, 44454274055540034471036, 2399751878355335217728304
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Row 4 of A262849.

Examples

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

Crossrefs

Cf. A262849.

A262848 Number of (n+2)X(6+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

4536, 352880, 17912392, 661066920, 26232879096, 1007501698644, 37291148287704, 1391736921064152
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Column 6 of A262849.

Examples

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

Crossrefs

Cf. A262849.

A262854 Number of (5+2)X(n+2) 0..1 arrays with each row divisible by 7 and column not divisible by 7, read as a binary number with top and left being the most significant bits.

Original entry on oeis.org

109, 1264, 31512, 3896365, 290338650, 26232879096, 2864161217701, 297481646988280
Offset: 1

Views

Author

R. H. Hardin, Oct 03 2015

Keywords

Comments

Row 5 of A262849.

Examples

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

Crossrefs

Cf. A262849.
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