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A307939 Number of (undirected) Hamiltonian paths in the n-dipyramidal graph. 1
36, 120, 310, 660, 1218, 2032, 3150, 4620, 6490, 8808, 11622, 14980, 18930, 23520, 28798, 34812, 41610, 49240, 57750, 67188, 77602, 89040, 101550, 115180, 129978, 145992, 163270, 181860, 201810, 223168, 245982, 270300, 296170, 323640, 352758, 383572, 416130, 450480 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Colin Barker, Table of n, a(n) for n = 3..1000

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Hamiltonian Path

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 2*n*(31 - 20*n + 4*n^2) for n > 3.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 7.

G.f.: 2*x^3*(18 - 12*x + 23*x^2 - 2*x^3 - 3*x^4) / (1 - x)^4. - Colin Barker, May 09 2019

MATHEMATICA

Join[{36}, Table[2 n (31 - 20 n + 4 n^2), {n, 4, 20}]]

Join[{36}, LinearRecurrence[{4, -6, 4, -1}, {120, 310, 660, 1218}, 20]]

CoefficientList[Series[-2 (-18 + 12 x - 23 x^2 + 2 x^3 + 3 x^4)/(-1 + x)^4, {x, 0, 20}], x]

PROG

(PARI) Vec(2*x^3*(18 - 12*x + 23*x^2 - 2*x^3 - 3*x^4) / (1 - x)^4 + O(x^40)) \\ Colin Barker, May 09 2019

CROSSREFS

Sequence in context: A287861 A242356 A165966 * A254146 A173420 A271736

Adjacent sequences:  A307936 A307937 A307938 * A307940 A307941 A307942

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, May 06 2019

STATUS

approved

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Last modified August 9 04:30 EDT 2020. Contains 336319 sequences. (Running on oeis4.)