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
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.
- Steve Butler, Table of n, a(n) for n = 1..135
- Esther Banaian, Steve Butler, Christopher Cox, Jeffrey Davis, Jacob Landgraf, Scarlitte Ponce, Counting prime juggling patterns, arXiv:1508.05296 [math.CO], 2015.
- Fan Chung and R. L. Graham, Primitive juggling sequences, American Mathematical Monthly 115 (2008), 185-194.
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
-
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 *)
Comments