A228770 The number of sum indecomposable permutations which avoid the patterns 3124 and 4312.

1, 1, 3, 12, 51, 217, 912, 3785, 15554, 63458, 257566, 1041548, 4200462, 16906262, 67943341, 272740788, 1093881967, 4384217569, 17562176283, 70319782015, 281466691159, 1126304935761, 4505961410365, 18023526090613, 72082118816829, 288245594631227, 1152536796877409, 4607992736095739, 18422141293792669, 73645313049839723

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013)

Formula

G.f.: -(24*x^6 - 71*x^5 + 84*x^4 - 45*x^3 + 11*x^2 + sqrt(-4*x + 1)*(4*x^6 - 25*x^5 + 40*x^4 - 29*x^3 + 9*x^2 - x) - x)/(8*x^6 - 54*x^5 + 117*x^4 - 114*x^3 + 54*x^2 - sqrt(-4*x + 1)*(12*x^5 - 43*x^4 + 58*x^3 - 36*x^2 + 10*x - 1) - 12*x + 1).

a(n) ~ 2^(2*n-1)/9 * (1+2/(sqrt(Pi*n))). - Vaclav Kotesovec, Mar 20 2014

Conjecture: -(n+1)*(39961*n-2474598)*a(n) +(-39961*n^2-25975201*n+4949196) *a(n-1) +3*(1460811*n^2+27429105*n-41310802) *a(n-2) +3 *(-8653921*n^2-4750029*n+74360724) *a(n-3) +4*(15005713*n^2-82481258*n+83094771) *a(n-4) +12*(-4937548*n^2+40726604*n-73155719) *a(n-5) +16*(652718*n-2110173)*(2*n-13) *a(n-6)=0. - R. J. Mathar, Jun 14 2016

Example

Example: a(4)=12 because there are 12 sum indecomposable permutations of length 4 which avoid the patterns 3124 and 4312.

Mathematica

CoefficientList[Series[- (1/x) (24 x^6 - 71 x^5 + 84 x^4 - 45 x^3 + 11 x^2 + Sqrt[-4 x + 1] (4 x^6 - 25 x^5 + 40 x^4 - 29 x^3 + 9 x^2 - x) - x) / (8 x^6 - 54 x^5 + 117 x^4 - 114 x^3 + 54 x^2 - Sqrt[-4 x + 1] (12 x^5 - 43 x^4 + 58 x^3 - 36 x^2 + 10 x - 1) - 12 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 09 2013 *)

Crossrefs

A228770(n) = A165534(n) - A226434(n)

Sequence in context: A135343 A083314 A155179 * A104268 A081704 A166482

Adjacent sequences: A228767 A228768 A228769 * A228771 A228772 A228773

Keyword

nonn

Author

Jay Pantone, Sep 08 2013

Status

approved