A386907 Number of spanning trees of the class H_3.

75, 336, 1488, 6580, 29085, 128544, 568101, 2510716, 11096064, 49038840, 216726195, 957817168, 4233054171, 18707899800, 82679195856, 365399082748, 1614874071885, 7136904253920, 31541408222709, 139396634349556, 616060688564736, 2722668117245424, 12032778286721955

Offset

0,1

Comments

See Blanco-Zeilberger paper.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1546

Pablo Blanco and Doron Zeilberger, Powers of Cycles and Paths: The Generating Functions for Enumerating Their Spanning Trees, Rutgers Univ. (2025). See p. 6.

Index entries for linear recurrences with constant coefficients, signature (5,-3,3,-5,1). [Corrected by Georg Fischer, Aug 13 2025]

Formula

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)).

Mathematica

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]

Crossrefs

Cf. A001906, A386908.

Sequence in context: A158765 A226741 A223078 * A055561 A350245 A193252

Adjacent sequences: A386904 A386905 A386906 * A386908 A386909 A386910

Keyword

nonn,easy

Author

Michael De Vlieger, Aug 07 2025

Status

approved