A229734 G.f.: (1+x-2*x^2+2*x^3-sqrt(1-2*x-3*x^2+4*x^3-4*x^4))/(2*(1-x+x^2)).

0, 1, 1, 1, 2, 3, 7, 14, 33, 73, 174, 407, 987, 2386, 5877, 14509, 36210, 90715, 228863, 579654, 1475465, 3768993, 9664454, 24857951, 64133027, 165900202, 430242509, 1118325365, 2913106746, 7603261427, 19881409943, 52076282638, 136625968593, 358989196793, 944595607198, 2488799333031, 6565694568171

Offset

0,5

Links

Table of n, a(n) for n=0..36.

S. Kitaev and J. Remmel, The 1-box pattern on pattern avoiding permutations, arXiv preprint arXiv:1305.6970 [math.CO], 2013. See Th. 8. also J. Int. Seq. 17 (2014) 14.3.3

Formula

D-finite with recurrence: n*a(n) +3*(-n+1)*a(n-1) +6*a(n-2) +(5*n-24)*a(n-3) +(-11*n+51)*a(n-4) +2*(4*n-21)*a(n-5) +4*(-n+6)*a(n-6)=0. - R. J. Mathar, Jan 24 2018

Mathematica

CoefficientList[Series[(1+x-2x^2+2x^3-Sqrt[1-2x-3x^2+4x^3-4x^4])/(2(1-x+ x^2)), {x, 0, 40}], x] (* Harvey P. Dale, Apr 28 2016 *)

Crossrefs

Sequence in context: A180752 A000642 A348530 * A035083 A328057 A305785

Adjacent sequences: A229731 A229732 A229733 * A229735 A229736 A229737

Keyword

nonn

Author

N. J. A. Sloane, Oct 01 2013

Status

approved