A055341 Number of mobiles (circular rooted trees) with n nodes and 3 leaves.

1, 3, 8, 19, 37, 66, 110, 172, 257, 371, 518, 705, 939, 1226, 1574, 1992, 2487, 3069, 3748, 4533, 5435, 6466, 7636, 8958, 10445, 12109, 13964, 16025, 18305, 20820, 23586, 26618, 29933, 33549, 37482, 41751, 46375, 51372, 56762, 62566, 68803, 75495, 82664, 90331

Offset

4,2

Links

Stefano Spezia, Table of n, a(n) for n = 4..10000

Index entries for sequences related to mobiles

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,0,1,2,-3,1).

Formula

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

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) - 3*a(n-7) + a(n-8). - Wesley Ivan Hurt, Jan 06 2026

Maple

A055341 := proc(n)
    n^2/12+n/2-215/288+n^4/48-n^3/9-(-1)^n/32-2*A049347(n)/9 ;
end proc:
seq(A055341(n), n=4..40 ) ; # reuses code of A049347 R. J. Mathar, Feb 14 2025

Mathematica

CoefficientList[Series[(-x^4 + 2*x^3 + x^2 + 1)/((1 - x^2)*(1 - x^3)*(1 - x)^3), {x, 0, 60}], x] (* Wesley Ivan Hurt, Jan 06 2026 *)

Crossrefs

Column 3 of A055340.

Sequence in context: A209367 A086167 A083186 * A067332 A082535 A007326

Adjacent sequences: A055338 A055339 A055340 * A055342 A055343 A055344

Keyword

nonn,easy

Author

Christian G. Bower, May 14 2000

Extensions

Terms a(45) onward from Stefano Spezia, Jan 10 2026

Status

approved