A212199 Expansion of (1 + 3*x + 4*x^2 - sqrt(1 - 2*x - 7*x^2))/(4 + 8*x).

0, 1, 0, 1, 1, 5, 11, 39, 113, 377, 1207, 4043, 13509, 45957, 157171, 542671, 1884665, 6586993, 23137647, 81662355, 289414157, 1029598333, 3675337963, 13160833623, 47261437761, 170164260713, 614154154791, 2221545593179, 8052506141653, 29244341625077, 106397352342243, 387745600670175, 1415284544031241, 5173441096267489, 18937206005320415, 69409364862108451

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Sergey Kitaev, Pavel Salimov, Christopher Severs, and Henning Ulfarsson, Restricted rooted non-separable planar maps, arXiv:1202.1790 [math.CO], 2012.

S. Kitaev, P. Salimov, C. Severs and H. Ulfarsson, Restricted non-separable planar maps and some pattern avoiding permutations, preprint 2012. [N. J. A. Sloane, Jan 01 2013]

Formula

a(n) ~ sqrt(44-31*sqrt(2))*(1+2*sqrt(2))^n/(4*n^(3/2)*sqrt(Pi)). - Vaclav Kotesovec, Jun 29 2013

D-finite with recurrence: n*a(n) +3*a(n-1) -(11*n-27)*a(n-2) -14*(n-3)*a(n-3) = 0 for n>4. - Bruno Berselli, Jul 18 2013

Let T(n, k) = 2^k*binomial(n-k, k)*hypergeom([-k, k-n-1], [2], 1) then

a(n) = Sum_{k=0..(n-3)/2} T(n-3, k) if n != 1. - Peter Luschny, Oct 19 2020

Maple

T := (n, k) -> simplify(2^k*binomial(n-k, k)*hypergeom([-k, k-n-1], [2], 1)):
[0, 1, 0, seq(add(T(n, k), k=0..floor(n/2)), n=0..32)]; # Peter Luschny, Oct 19 2020

Mathematica

CoefficientList[Series[(1 + 3 x + 4 x^2 - Sqrt[1 - 2 x - 7 x^2]) / (4 + 8 x), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 18 2013 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec((1+3*x+4*x^2-sqrt(1-2*x-7*x^2))/(4+8*x))) \\ G. C. Greubel, Mar 30 2017

Crossrefs

Sequence in context: A197337 A302766 A369982 * A276663 A187984 A063626

Adjacent sequences: A212196 A212197 A212198 * A212200 A212201 A212202

Keyword

nonn

Author

N. J. A. Sloane, May 11 2012

Status

approved