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 1-6 of 6 results.

A221454 Number of 0..3 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..3 order.

Original entry on oeis.org

0, 1, 2, 7, 24, 88, 328, 1235, 4668, 17675, 66974, 253858, 962352, 3648397, 13831870, 52440191, 198815196, 753764564, 2857736696, 10834499599, 41076702120, 155733594211, 590430871282, 2238493367822, 8486772670944, 32175798041273
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Column 3 of A221459.

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..1....2....2....1....0....2....2....2....1....2....2....2....2....2....2....2
..0....2....3....2....1....0....1....3....2....1....1....1....3....2....3....0
..0....1....2....2....2....1....3....3....1....2....2....0....3....0....1....0
..1....3....1....0....0....3....1....2....2....3....0....3....1....3....2....1

Links

Crossrefs

Cf. A221459.

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4).
Empirical g.f.: x^2*(1 - 2*x - 2*x^2) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Mar 14 2018

A221453 Number of 0..n arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..n order.

Original entry on oeis.org

0, 1, 2, 7, 25, 102, 456, 2219, 11640, 65364, 390646, 2472719, 16508791, 115839661, 851634863, 6542134884, 52384882759, 436290809772, 3772143122161, 33797290492507, 313304547351868, 3000631062271288, 29651208549845055
Offset: 1

Views

Author

R. H. Hardin Jan 17 2013

Keywords

Comments

Diagonal of A221459

Examples

			Some solutions for n=6
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..0....2....1....0....2....2....1....0....2....2....0....1....0....1....1....1
..2....1....2....1....3....0....2....2....1....3....2....2....1....2....2....0
..2....3....1....1....0....0....2....3....2....2....1....2....2....1....3....0
..3....4....2....2....3....3....1....0....3....0....2....0....0....3....0....1

Links

A221455 Number of 0..4 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..4 order.

Original entry on oeis.org

0, 1, 2, 7, 25, 101, 436, 1971, 9159, 43262, 206285, 988963, 4755888, 22910979, 110480787, 533057462, 2572761417, 12419474751, 59958562568, 289483787719, 1397691920591, 6748491159958, 32584154032229, 157329000870907
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Column 4 of A221459.

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..1....2....0....0....2....2....2....2....2....2....2....0....2....0....1....2
..0....1....2....2....1....3....2....1....0....3....0....0....3....2....2....0
..1....1....2....3....3....4....3....3....1....0....3....2....2....2....3....3
..0....2....3....1....2....0....4....0....0....2....2....1....1....0....2....1

Links

Crossrefs

Cf. A221459.

Formula

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6).
Empirical g.f.: x^2*(1 - 5*x + 10*x^3 + 5*x^4) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Aug 05 2018

A221456 Number of 0..5 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..5 order.

Original entry on oeis.org

0, 1, 2, 7, 25, 102, 455, 2192, 11203, 59814, 329343, 1851911, 10560334, 60776590, 351887190, 2045329031, 11918417465, 69563676328, 406447507101, 2376416054328, 13900548090293, 81332697848104, 475968841105687, 2785759950405621
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Column 5 of A221459.

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....0....2....2....1....2....2....0....1....1....2....2....2....0....2
..2....1....0....2....0....0....1....1....2....0....2....2....0....3....2....3
..3....3....2....0....3....0....0....1....1....2....3....1....0....4....0....3
..2....4....3....3....0....2....1....2....0....1....1....3....1....0....2....4

Links

Crossrefs

Cf. A221459.

Formula

Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8).
Empirical g.f.: x^2*(1 - 9*x + 15*x^2 + 29*x^3 - 33*x^4 - 57*x^5 - 19*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - Colin Barker, Aug 05 2018

A221457 Number of 0..6 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..6 order.

Original entry on oeis.org

0, 1, 2, 7, 25, 102, 456, 2218, 11605, 64647, 379349, 2320555, 14658240, 94843284, 624544847, 4164947151, 28025750099, 189783308469, 1290899153376, 8808076870934, 60230644078721, 412493027114619, 2827998455493193
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Column 6 of A221459.

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....2....2....2....2....1....2....1....2....2....0....2....0....2....2
..1....0....1....3....1....3....2....3....0....1....0....2....2....2....3....1
..3....3....2....1....2....0....2....2....0....0....2....0....0....3....2....2
..1....2....3....2....0....4....3....1....1....1....3....1....1....4....4....1

Links

Crossrefs

Cf. A221459.

Formula

Empirical: a(n) = 16*a(n-1) - 79*a(n-2) + 70*a(n-3) + 361*a(n-4) - 372*a(n-5) - 964*a(n-6) + 144*a(n-7) + 1116*a(n-8) + 720*a(n-9) + 144*a(n-10).
Empirical g.f.: x^2*(1 - 14*x + 54*x^2 + x^3 - 246*x^4 - 41*x^5 + 411*x^6 + 364*x^7 + 91*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 4*x - 4*x^2)*(1 - 6*x - 6*x^2)). - Colin Barker, Aug 05 2018

A221458 Number of 0..7 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..7 order.

Original entry on oeis.org

0, 1, 2, 7, 25, 102, 456, 2219, 11639, 65320, 389533, 2451393, 16164044, 110866328, 785411383, 5709898562, 42358751505, 319155928942, 2433165471304, 18714220718157, 144885627697659, 1127182676182780, 8800901309557829
Offset: 1

Views

Author

R. H. Hardin Jan 17 2013

Keywords

Comments

Column 7 of A221459

Examples

			Some solutions for n=6
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....1....1....2....0....2....0....0....2....1....1....0....2....2....0....2
..3....2....0....3....1....2....1....2....0....2....2....0....0....2....0....1
..0....1....0....3....2....1....2....2....3....0....2....2....1....3....2....1
..2....0....2....2....1....0....3....1....4....3....0....0....0....1....1....0

Links

Formula

Empirical: a(n) = 22*a(n-1) -168*a(n-2) +440*a(n-3) +421*a(n-4) -2898*a(n-5) -924*a(n-6) +7944*a(n-7) +5931*a(n-8) -6610*a(n-9) -10562*a(n-10) -5040*a(n-11) -840*a(n-12)
Showing 1-6 of 6 results.

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