A386907 - OEIS

%I #11 Aug 13 2025 10:19:44

%S 75,336,1488,6580,29085,128544,568101,2510716,11096064,49038840,

%T 216726195,957817168,4233054171,18707899800,82679195856,365399082748,

%U 1614874071885,7136904253920,31541408222709,139396634349556,616060688564736,2722668117245424,12032778286721955

%N Number of spanning trees of the class H_3.

%C See Blanco-Zeilberger paper.

%H Michael De Vlieger, <a href="/A386907/b386907.txt">Table of n, a(n) for n = 0..1546</a>

%H Pablo Blanco and Doron Zeilberger, <a href="https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/sptOld.pdf">Powers of Cycles and Paths: The Generating Functions for Enumerating Their Spanning Trees</a>, Rutgers Univ. (2025). See p. 6.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-3,3,-5,1). [Corrected by _Georg Fischer_, Aug 13 2025]

%F G.f.: (-16*x^4 + 77*x^3 - 33*x^2 + 39*x - 75)/((x - 1)*(x^4 - 4*x^3 - x^2 - 4*x + 1)).

%t CoefficientList[Series[(-16*x^4 + 77*x^3 - 33*x^2 + 39*x - 75)/((x - 1)*(x^4 - 4*x^3 - x^2 - 4*x + 1)), {x, 0, 12}], x]

%Y Cf. A001906, A386908.

%K nonn,easy

%O 0,1

%A _Michael De Vlieger_, Aug 07 2025