A036908 Number of different compact source directed animals with 1 point on the bottom line.

1, 2, 5, 14, 40, 116, 339, 996, 2937, 8684, 25729, 76352, 226868, 674806, 2008907, 5984886, 17841024, 53212500, 158784033, 473995320, 1415449578, 4228149450, 12633596331, 37758241434, 112873961079, 337492122822, 1009283640669, 3018807519506, 9030752740042

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Nickolas Hein and Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.

Formula

G.f.: x^2*(1-3*x+sqrt(1-2*x-3*x^2))/((1-3*x)*(3*x-1+sqrt(1-2*x-3*x^2))). - amended by Georg Fischer, Apr 09 2020

D-finite with recurrence: (-n+1)*a(n) +(5*n-8)*a(n-1) +3*(-n+1)*a(n-2) +9*(-n+4)*a(n-3)=0. - R. J. Mathar, Jan 28 2020

a(n) ~ 3^(n-2) * (1 + sqrt(3/(Pi*n))). - Vaclav Kotesovec, Apr 09 2020

Mathematica

Rest[CoefficientList[Series[x^2*(1-3*x+Sqrt[1-2*x-3*x^2])/((1-3*x)*(3x-1+Sqrt[1- 2*x-3*x^2])), {x, 0, 30}], x]] (* Harvey P. Dale, Jun 03 2012; Georg Fischer, Apr 09 2020 *)

Prog

(PARI) seq(n)={my(p=sqrt(1-2*x-3*x^2 + O(x*x^n))); Vec(x^2*(1-3*x+p)/((1-3*x)*(3*x-1+p)))} \\ Andrew Howroyd, Apr 09 2020

Crossrefs

Sequence in context: A117189 A052963 A329275 * A293346 A273900 A126220

Adjacent sequences: A036905 A036906 A036907 * A036909 A036910 A036911

Keyword

nonn

Author

Louis Shapiro

Extensions

More terms from Harvey P. Dale, Jun 03 2012

Status

approved