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 1-5 of 5 results.

A242467 Number of length n+2 0..n arrays with no three equal elements in a row and new values 0..n introduced in 0..n order.

Original entry on oeis.org

3, 11, 40, 158, 684, 3232, 16533, 90862, 533013, 3319374, 21844874, 151329961, 1099822975, 8361244270, 66320787389, 547602710173, 4697109624463, 41777867546600, 384671271459042, 3661037447467530, 35965775221739498
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Comments

Diagonal of A242472.

Examples

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

Links

Crossrefs

Cf. A242472.

A242468 Number of length n+2 0..5 arrays with no three equal elements in a row and new values 0..5 introduced in 0..5 order.

Original entry on oeis.org

4, 12, 41, 159, 684, 3204, 16042, 84412, 460174, 2570411, 14593499, 83749169, 484000704, 2809880001, 16360962717, 95445840289, 557493277222, 3258874744858, 19059827706050, 111510210083018, 652534784892188, 3819030330465099
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A242472.

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*(4 - 32*x + 29*x^2 + 152*x^3 - 31*x^4 - 285*x^5 - 215*x^6 - 49*x^7) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - Colin Barker, Nov 01 2018

A242469 Number of length n+2 0..6 arrays with no three equal elements in a row and new values 0..6 introduced in 0..6 order.

Original entry on oeis.org

4, 12, 41, 159, 685, 3232, 16497, 90075, 520248, 3143900, 19678699, 126480319, 828889655, 5508880129, 36980189248, 249999755818, 1698491520413, 11579658486155, 79137696973965, 541762392142995, 3713215153801152
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Comments

Column 6 of A242472

Examples

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

Links

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)

A242470 Number of length n+2 0..7 arrays with no three equal elements in a row and new values 0..7 introduced in 0..7 order.

Original entry on oeis.org

4, 12, 41, 159, 685, 3233, 16533, 90817, 531812, 3295779, 21456363, 145645809, 1023308083, 7391587656, 54563960012, 409583330514, 3113836080693, 23899707589707, 184747234605277, 1435668152296255, 11200152289621048
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Comments

Column 7 of A242472

Examples

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

A242471 Number of length n+2 0..8 arrays with no three equal elements in a row and new values 0..8 introduced in 0..8 order.

Original entry on oeis.org

4, 12, 41, 159, 685, 3233, 16534, 90862, 532958, 3317613, 21803646, 150528288, 1086089333, 8146481406, 63182485967, 504037166445, 4115582321241, 34244236336515, 289252828167957, 2472398717507023, 21329556857593204
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Comments

Column 8 of A242472

Examples

			Some solutions for n=5
..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....0....1....1....1....1....1....0
..2....2....2....1....2....1....2....1....2....1....2....1....1....2....2....1
..3....3....2....2....2....0....3....2....3....2....3....2....0....3....3....2
..0....0....3....2....1....2....0....2....4....3....2....2....1....0....4....0
..4....4....4....0....2....2....2....3....2....4....0....1....1....3....1....3
..0....5....4....1....1....3....4....3....1....3....4....3....2....1....2....1

Links

Formula

Empirical: a(n) = 29*a(n-1) -314*a(n-2) +1449*a(n-3) -1442*a(n-4) -8855*a(n-5) +16059*a(n-6) +34312*a(n-7) -42104*a(n-8) -101900*a(n-9) -6124*a(n-10) +112608*a(n-11) +106128*a(n-12) +40320*a(n-13) +5760*a(n-14)
Showing 1-5 of 5 results.

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