A293775 Number of permutations of length n sortable by 4 passes through a pop-stack.

1, 1, 2, 6, 24, 120, 565, 2473, 10468, 44148, 187363, 799605, 3418967, 14615713, 62439735, 266643093, 1138577340, 4862025964, 20763336212, 88672294260, 378685960241, 1617214869969, 6906440938924, 29494450730730, 125958207787945, 537914052728909

Offset

0,3

Links

Bjarki Ágúst Guðmundsson, Table of n, a(n) for n = 0..1000

Anders Claesson, Bjarki Ágúst Guðmundsson, Enumerating permutations sortable by k passes through a pop-stack, arXiv:1710.04978 [math.CO], 2017.

Formula

G.f.: (64*x^25 + 448*x^24 + 1184*x^23 + 1784*x^22 + 2028*x^21 + 1948*x^20 + 1080*x^19 + 104*x^18 - 180*x^17 + 540*x^16 + 1156*x^15 + 696*x^14 + 252*x^13 + 238*x^12 + 188*x^11 + 502*x^10 + 806*x^9 + 544*x^8 + 263*x^7 + 185*x^6 + 99*x^5 + 33*x^4 + 13*x^3 + 3*x^2 + x - 1) / (128*x^25 + 896*x^24 + 2368*x^23 + 3568*x^22 + 3928*x^21 + 3064*x^20 + 176*x^19 - 2304*x^18 - 2664*x^17 - 1580*x^16 - 352*x^15 - 576*x^14 - 1104*x^13 - 760*x^12 - 138*x^11 + 686*x^10 + 1238*x^9 + 869*x^8 + 382*x^7 + 210*x^6 + 102*x^5 + 27*x^4 + 12*x^3 + 3*x^2 + 2*x - 1).

Prog

(PARI) Vec((64*x^25 + 448*x^24 + 1184*x^23 + 1784*x^22 + 2028*x^21 + 1948*x^20 + 1080*x^19 + 104*x^18 - 180*x^17 + 540*x^16 + 1156*x^15 + 696*x^14 + 252*x^13 + 238*x^12 + 188*x^11 + 502*x^10 + 806*x^9 + 544*x^8 + 263*x^7 + 185*x^6 + 99*x^5 + 33*x^4 + 13*x^3 + 3*x^2 + x - 1)/(128*x^25 + 896*x^24 + 2368*x^23 + 3568*x^22 + 3928*x^21 + 3064*x^20 + 176*x^19 - 2304*x^18 - 2664*x^17 - 1580*x^16 - 352*x^15 - 576*x^14 - 1104*x^13 - 760*x^12 - 138*x^11 + 686*x^10 + 1238*x^9 + 869*x^8 + 382*x^7 + 210*x^6 + 102*x^5 + 27*x^4 + 12*x^3 + 3*x^2 + 2*x - 1) + O(x^30))

Crossrefs

Cf. A224232, A293774, A293776, A293784.

Sequence in context: A228401 A189861 A189570 * A228399 A179340 A179342

Adjacent sequences: A293772 A293773 A293774 * A293776 A293777 A293778

Keyword

nonn,easy

Author

Bjarki Ágúst Guðmundsson, Oct 16 2017

Status

approved