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 13 results. Next

A212226 Number of 0..2 arrays of length n+3 with sum no more than 4 in any length 4 subsequence (=50% duty cycle).

Original entry on oeis.org

50, 124, 311, 775, 1895, 4663, 11518, 28446, 70145, 172951, 426630, 1052487, 2596184, 6403675, 15795627, 38963018, 96109484, 237070048, 584773118, 1442444418, 3558040343, 8776520278, 21648797430, 53400493513, 131721540000
Offset: 1

Views

Author

R. H. Hardin, May 06 2012

Keywords

Comments

Column 2 of A212232.

Examples

			Some solutions for n=3
..0....0....2....1....0....1....1....1....0....1....1....0....1....1....1....1
..0....1....1....2....1....2....1....1....1....0....1....2....2....1....0....0
..1....0....1....1....0....0....2....0....0....0....0....2....0....1....1....0
..0....0....0....0....0....1....0....1....0....2....2....0....1....1....0....1
..2....0....2....0....2....0....1....0....1....1....1....0....1....0....2....2
..1....0....1....0....0....0....1....1....0....1....0....2....2....1....1....0

Links

Crossrefs

Cf. A212232.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-3) +6*a(n-4) -3*a(n-5) -a(n-6) +a(n-7) -7*a(n-8) +4*a(n-9) -a(n-10) +3*a(n-12) -4*a(n-13) -a(n-16) +a(n-17).

A212227 Number of 0..2 arrays of length n+5 with sum no more than 6 in any length 6 subsequence (=50% duty cycle).

Original entry on oeis.org

435, 1113, 2902, 7596, 19834, 51440, 131950, 339564, 876777, 2267261, 5864274, 15159987, 39161060, 101136977, 261240954, 674934552, 1743897567, 4505828919, 11641402990, 30075908053, 77701600604, 200746256554, 518645274018
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Column 3 of A212232

Examples

			Some solutions for n=3
..1....0....2....1....1....1....1....0....2....0....2....2....2....0....0....0
..0....0....1....1....2....1....0....1....0....1....0....0....2....1....0....0
..0....2....0....1....1....2....0....0....2....0....1....0....0....0....1....0
..0....0....1....1....1....0....1....2....0....0....2....2....1....0....1....0
..2....2....0....0....0....1....2....2....1....1....0....0....1....2....0....0
..1....0....2....0....0....1....1....0....0....1....1....2....0....1....2....2
..0....1....1....1....2....0....0....0....0....1....2....1....2....0....0....2
..1....0....1....1....0....2....0....0....0....0....0....0....1....1....1....1

Links

A212228 Number of 0..2 arrays of length n+7 with sum no more than 8 in any length 8 subsequence (=50% duty cycle).

Original entry on oeis.org

3834, 10002, 26637, 71427, 191853, 514687, 1376128, 3659968, 9662878, 25562476, 67800449, 180120882, 478897973, 1273545563, 3386125989, 8999257525, 23906208533, 63493578634, 168644397152, 447996097328, 1190222549456
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Column 4 of A212232

Examples

			Some solutions for n=3
..0....0....0....0....1....2....2....0....0....2....2....1....1....0....1....0
..1....2....0....1....0....1....0....1....1....2....0....2....2....2....1....0
..1....0....0....1....0....1....1....2....0....1....1....0....0....0....1....0
..1....0....2....0....1....0....0....0....1....0....1....1....0....0....2....1
..2....0....2....0....0....0....1....0....1....0....2....0....1....1....0....0
..1....1....0....0....1....1....2....2....2....1....0....2....2....0....1....1
..2....2....0....1....1....2....0....2....0....1....0....2....1....0....1....0
..0....1....2....1....0....0....2....0....1....1....0....0....1....1....0....0
..0....1....2....1....0....2....1....1....1....2....1....1....1....1....1....2
..0....2....0....2....2....0....0....0....2....2....1....2....0....1....0....2

Links

A212229 Number of 0..2 arrays of length n+9 with sum no more than 10 in any length 10 subsequence (=50% duty cycle).

Original entry on oeis.org

34001, 89911, 242780, 660796, 1804448, 4931630, 13468524, 36711516, 99762134, 269986256, 726810250, 1959270880, 5292416365, 14316932524, 38765529832, 105016326560, 284539410032, 770899685027, 2088100303095, 5654125322731
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Column 5 of A212232

Examples

			Some solutions for n=3
..0....0....0....0....0....0....0....1....0....1....0....0....0....0....0....0
..1....0....0....1....0....2....0....0....0....0....0....0....0....0....2....1
..0....1....2....2....0....0....0....0....0....0....2....0....0....0....0....2
..1....1....0....1....0....1....2....0....0....1....2....2....1....1....2....0
..2....1....1....0....0....0....2....0....1....1....2....2....2....1....0....0
..0....0....0....1....2....2....1....1....2....1....0....0....1....0....2....2
..0....0....0....1....0....2....0....2....1....0....0....1....0....0....2....1
..2....1....1....1....1....2....2....0....1....1....0....0....1....1....2....0
..2....0....0....0....0....0....0....1....1....0....2....1....2....1....0....0
..0....0....2....2....2....0....0....1....1....1....1....2....1....0....0....2
..2....0....1....1....2....0....0....1....0....0....1....1....0....1....0....0
..1....1....2....1....1....1....1....0....1....0....0....0....2....2....0....2

Links

A212230 Number of 0..2 arrays of length n+11 with sum no more than 12 in any length 12 subsequence (=50% duty cycle).

Original entry on oeis.org

302615, 808403, 2204646, 6062948, 16740414, 46305966, 128148456, 354470546, 979272751, 2700150083, 7425872754, 20355794336, 55576133157, 151888056136, 415782103202, 1139624300299, 3126418458642, 8581964181953, 23565242287322
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Column 6 of A212232

Examples

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....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....2....0....1....0....0....0....0....0....1....1....0....0....1
..1....1....1....0....0....0....2....1....2....1....0....2....0....1....1....0
..0....2....1....0....1....1....2....1....1....0....2....1....0....1....0....1
..2....0....2....2....0....1....0....0....1....1....0....0....1....2....2....1
..2....1....1....1....2....1....1....2....0....0....1....1....1....2....1....2
..1....2....0....2....2....2....0....2....0....1....2....0....0....0....1....0
..0....0....0....1....1....0....0....0....0....2....0....1....0....2....1....1
..1....1....2....2....1....0....1....1....1....2....1....0....0....1....0....2
..1....1....1....0....2....1....0....2....2....1....0....0....2....1....0....2
..1....2....2....0....0....2....1....0....0....0....0....2....1....0....1....1
..0....1....0....2....1....2....0....1....0....1....0....2....0....1....2....1

Links

A212231 Number of 0..2 arrays of length n+13 with sum no more than 14 in any length 14 subsequence (=50% duty cycle).

Original entry on oeis.org

2699598, 7269626, 19976155, 55360211, 154089343, 429886243, 1200645159, 3354267511, 9367667604, 26139182862, 72841658426, 202630826716, 562443898300, 1557047060794, 4296908081691, 11867091374754, 32817710013245
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Column 7 of A212232

Examples

			Some solutions for n=3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....1....0....1....0....0....1....0....0....1....1....1....1....1
..1....2....0....1....0....1....1....1....0....0....0....1....2....1....2....0
..2....1....1....1....2....0....0....0....2....1....2....2....0....2....0....1
..2....2....1....1....0....2....0....0....2....2....0....2....1....2....2....0
..0....2....2....2....0....2....1....2....0....1....2....0....2....0....1....2
..2....0....0....1....2....2....0....1....0....0....0....0....2....1....1....1
..1....0....1....0....0....2....2....1....0....1....0....2....0....0....0....0
..0....1....2....1....1....1....0....2....1....0....1....1....2....0....1....1
..0....1....1....2....1....0....0....2....1....1....1....0....1....1....1....2
..2....0....2....2....0....2....0....0....2....2....2....2....1....0....1....2
..2....0....0....1....0....0....2....0....1....1....2....0....2....0....2....1

Links

A212233 Number of 0..2 arrays of length 2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

6, 50, 435, 3834, 34001, 302615, 2699598, 24121674, 215786649, 1932081885, 17311097568, 155188936431, 1391839527240, 12487516404434, 112071578930795, 1006067340461802, 9033468257955009, 81126883587357557, 728697257578499280
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Row 1 of A212232.

Examples

			Some solutions for n=3
..2....1....2....1....0....1....1....0....0....0....1....0....1....1....0....0
..0....0....0....0....2....0....2....2....0....2....1....1....1....0....1....2
..2....2....0....1....1....2....0....0....1....1....0....2....1....1....1....0
..1....1....1....1....0....0....1....2....0....0....1....2....0....0....1....0
..0....0....0....1....2....1....1....1....1....2....1....1....0....1....0....1
..1....0....1....1....0....1....1....0....2....1....0....0....2....2....1....1

Links

Crossrefs

Cf. A212232.

A212234 Number of 0..2 arrays of length 1+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

14, 124, 1113, 10002, 89911, 808403, 7269626, 65380788, 588072207, 5289869433, 47586806448, 428105244789, 3851528519268, 34652238703192, 311776035394625, 2805210936456962, 25240510718260791, 227111596463339585
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Row 2 of A212232

Examples

			Some solutions for n=3
..0....0....0....1....1....0....1....0....1....0....1....1....0....0....2....1
..0....0....0....1....0....2....1....2....0....2....1....0....0....1....1....1
..1....0....2....0....1....0....0....2....0....1....1....1....0....0....0....2
..2....1....1....2....1....0....2....0....0....0....2....2....2....0....1....0
..0....1....0....1....2....1....0....0....1....2....1....0....1....1....2....1
..2....1....1....0....1....1....1....0....2....0....0....0....0....1....0....0
..0....0....0....2....0....2....1....2....1....1....0....1....0....1....0....2

Links

Programs

  • Maple
    f:= proc(n) local S;
   S:= series((1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z), z, 2*n+1);
 coeff(S,z,2*n);
end proc:
map(f, [$1..50]); # Robert Israel, Mar 06 2018

Formula

a(n) = [x^(2*n)] (1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z). - Robert Israel, Mar 06 2018

A212235 Number of 0..2 arrays of length 2+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

31, 311, 2902, 26637, 242780, 2204646, 19976155, 180744711, 1633768428, 14757208260, 133224377745, 1202213897088, 10845157390965, 97807813761227, 881892198839574, 7950191559259765, 71659250039164212, 645816864760873772
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Row 3 of A212232

Examples

			Some solutions for n=3
..0....0....1....0....0....1....1....0....2....1....1....2....2....0....0....1
..0....1....0....1....1....0....1....2....2....0....1....1....0....2....0....1
..0....0....0....1....1....1....0....1....1....0....0....0....0....1....0....2
..0....1....0....0....1....0....0....0....0....0....0....0....0....0....2....0
..0....0....1....1....1....2....2....1....0....0....2....1....0....0....0....2
..0....1....1....0....2....0....1....1....0....0....1....0....1....0....2....0
..0....2....2....0....0....0....1....1....1....1....2....0....1....0....1....0
..1....1....1....1....1....0....2....1....2....2....1....2....0....0....1....1

Links

A212236 Number of 0..2 arrays of length 3+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).

Original entry on oeis.org

70, 775, 7596, 71427, 660796, 6062948, 55360211, 503916387, 4577086146, 41509589394, 376014757137, 3403088304192, 30777595344747, 278194559997967, 2513387971773920, 22698724065174107, 204927838029912468
Offset: 1

Views

Author

R. H. Hardin May 06 2012

Keywords

Comments

Row 4 of A212232

Examples

			Some solutions for n=3
..1....0....1....0....1....0....0....0....1....1....2....2....0....2....0....0
..0....2....2....2....2....2....0....1....0....2....1....1....2....0....0....0
..0....1....0....0....1....0....1....2....0....0....1....0....0....0....2....2
..2....0....0....2....0....1....1....1....2....2....1....1....0....0....0....2
..0....2....1....0....0....0....0....0....1....0....0....2....0....1....0....1
..1....0....1....0....1....1....0....1....0....0....1....0....0....2....0....0
..1....1....0....2....0....0....1....0....1....0....0....0....2....1....2....0
..1....1....2....1....0....2....1....1....0....2....1....0....2....1....0....1
..0....1....1....0....1....0....2....1....1....0....2....1....2....0....2....1

Links

Showing 1-10 of 13 results. Next

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