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A036908 Number of different compact source directed animals with 1 point on the bottom line. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 10:20 EDT 2022. Contains 356114 sequences. (Running on oeis4.)