A386908 Number of spanning trees of the class H_4.

864, 5635, 35840, 226080, 1424736, 8975232, 56531412, 356045600, 2242419040, 14122994787, 88948032416, 560203336285, 3528214538112, 22221034368624, 139950209558628, 881419864147200, 5551266971808376, 34962412626016064, 220196633083726032, 1386819546435968365, 8734322716128534368

Offset

0,1

Comments

See Blanco-Zeilberger paper.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1247

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 (7,-1,-25,31,-52,-84,300,-84,-52,31,-25,-1,7,-1).

Formula

G.f.: (-125*x^13 + 859*x^12 - 13*x^11 - 3141*x^10 + 3475*x^9 - 5968*x^8 - 11312*x^7 + 36080*x^6 - 5597*x^5 - 7893*x^4 + 2435*x^3 - 2741*x^2 - 413*x + 864)/((x^6 - 3*x^5 + 6*x^4 - 10*x^3 + 6*x^2 - 3*x + 1) (x^8 - 4*x^7 - 17*x^6 + 8*x^5 + 49*x^4 + 8*x^3 - 17*x^2 - 4*x + 1)).

Mathematica

CoefficientList[Series[(-125*x^13 + 859*x^12 - 13*x^11 - 3141*x^10 + 3475*x^9 - 5968*x^8 - 11312*x^7 + 36080*x^6 - 5597*x^5 - 7893*x^4 + 2435*x^3 - 2741*x^2 - 413*x + 864)/((x^6 - 3*x^5 + 6*x^4 - 10*x^3 + 6*x^2 - 3*x + 1) (x^8 - 4*x^7 - 17*x^6 + 8*x^5 + 49*x^4 + 8*x^3 - 17*x^2 - 4*x + 1)), {x, 0, 20}], x]

Crossrefs

Cf. A001906, A386907.

Sequence in context: A298327 A299220 A300034 * A064321 A210408 A299413

Adjacent sequences: A386905 A386906 A386907 * A386909 A386910 A386911

Keyword

nonn,easy

Author

Michael De Vlieger, Aug 07 2025

Status

approved