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.

User: Scarlitte Ponce

Scarlitte Ponce's wiki page.

Scarlitte Ponce has authored 2 sequences.

A260744 Number of prime juggling patterns of period n using 2 balls.

Original entry on oeis.org

1, 2, 5, 10, 23, 48, 105, 216, 467, 958, 2021, 4146, 8631, 17604, 36377, 73876, 151379, 306882, 625149, 1263294, 2563895, 5169544, 10454105, 21046800, 42451179, 85334982, 171799853, 344952010, 693368423, 1391049900, 2792734257
Offset: 1

Author

Scarlitte Ponce, Jul 30 2015

Keywords

Comments

A juggling pattern is prime if the closed walk corresponding to the pattern in the juggling state graph is a cycle.

Examples

			In siteswap notation, the prime juggling pattern(s) of length one is 2; of length two are 31 and 40; of length three are 330, 411, 420, 501, 600.
		

Crossrefs

A260582 Number of ways to place 2n rooks on n X n board, 2 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 4 rooks below the main diagonal.

Original entry on oeis.org

1, 72, 2438, 48965, 727982, 9002669, 98831244, 1001534339, 9604385112, 88600727292, 795108048465, 6995452987296, 60672964077315, 520801298224219, 4436874672072459, 37592602817393616, 317246106027904761, 2669508900483670024, 22415690107381454687
Offset: 3

Author

Scarlitte Ponce, Jul 29 2015

Keywords

Comments

a(n) is the number of minimal multiplex juggling patterns of period n using exactly 4 balls when we can catch/throw up to 2 balls at a time. (Minimal in the sense that the number of throws is between 0 and n-1.)

Crossrefs

Column k=4 of A269742.

Programs

  • Mathematica
    CoefficientList[Series[-(4584825 x^18 - 32402639 x^17 + 116197885 x^16 - 276109240 x^15 + 466638686 x^14 - 565360388 x^13 + 479478061 x^12 - 263101580 x^11 + 64737485 x^10 + 27721713 x^9 - 36043190 x^8 + 18319939 x^7 - 5637417 x^6 + 1094626 x^5 - 124221 x^4 + 5875 x^3 + 171 x^2 - 14 x - 1)/(19266000 x^22 - 234624000 x^21 + 1345258600 x^20 - 4829459800 x^19 + 12177772645 x^18 - 22934336190  x^17 + 33487611783 x^16 - 38844575208 x^15 + 36384232939 x^14 - 27820436326 x^13 + 17485343731 x^12 - 9066508172 x^11 + 3881838842 x^10 - 1369857572 x^9 + 396588486 x^8 - 93458208 x^7 + 17715207 x^6 - 2654590 x^5 + 306583 x^4 - 26260 x^3 + 1567 x^2 - 58 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 19 2015 *)

Formula

G.f.: -(4584825*x^21 - 32402639*x^20 + 116197885*x^19 - 276109240*x^18 + 466638686*x^17 - 565360388*x^16 + 479478061*x^15 - 263101580*x^14 + 64737485*x^13 + 27721713*x^12 - 36043190*x^11 + 18319939*x^10 - 5637417*x^9 + 1094626*x^8 - 124221*x^7 + 5875*x^6 + 171*x^5 - 14*x^4 - x^3)/(19266000*x^22 - 234624000*x^21 + 1345258600*x^20 - 4829459800*x^19 + 12177772645*x^18 - 22934336190*x^17 + 33487611783*x^16 - 38844575208*x^15 + 36384232939*x^14 - 27820436326*x^13 + 17485343731*x^12 - 9066508172*x^11 + 3881838842*x^10 - 1369857572*x^9 + 396588486*x^8 - 93458208*x^7 + 17715207*x^6 - 2654590*x^5 + 306583*x^4 - 26260*x^3 + 1567*x^2 - 58*x + 1).