A278023 G.f.: 2*x*(1-x*sqrt(1-4*x))/((1+2*x^2+sqrt(1-4*x))*sqrt(1-4*x)).

0, 1, 2, 8, 30, 109, 401, 1495, 5623, 21289, 81034, 309817, 1188932, 4576980, 17667647, 68359881, 265045494, 1029512644, 4005417845, 15606129991, 60885118375, 237816401610, 929909358659, 3639712494186, 14258889345834, 55906875628333, 219370377887309, 861389105627213, 3384600499000626

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

J. L. Baril, Avoiding patterns in irreducible permutations, Discrete Mathematics and Theoretical Computer Science, submitted 2014. See Table 3.

Formula

a(n) ~ 2^(2*n+2) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 10 2016

Conjecture: +n*(3*n^2-12*n+11) *a(n) -(3*n-5) *(3*n^2-9*n+4) *a(n-1) -2*(2*n-5) *(3*n^2-6*n+2) *a(n-2) +n *(3*n^2-12*n+11) *a(n-3) -2 *(2*n-5) *(3*n^2-6*n+2) *a(n-4)=0. - R. J. Mathar, Jun 24 2018

Mathematica

CoefficientList[Series[2*x*(1-x*Sqrt[1-4*x])/(Sqrt[1-4*x]*(1+2*x^2+Sqrt[1-4*x])), {x, 0, 20}], x] (* Vaclav Kotesovec, Nov 10 2016 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(2*x*(1-x*sqrt(1-4*x) )/( (1+ 2*x^2 +sqrt(1-4*x))*sqrt(1-4*x)))) \\ G. C. Greubel, Jun 05 2017

Crossrefs

Sequence in context: A127865 A199923 A230269 * A077839 A052530 A274798

Adjacent sequences: A278020 A278021 A278022 * A278024 A278025 A278026

Keyword

nonn

Author

N. J. A. Sloane, Nov 09 2016

Status

approved