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A060446 Number of ways to color vertices of a pentagon using <= n colors, allowing rotations and reflections. 8
0, 1, 8, 39, 136, 377, 888, 1855, 3536, 6273, 10504, 16775, 25752, 38233, 55160, 77631, 106912, 144449, 191880, 251047, 324008, 413049, 520696, 649727, 803184, 984385, 1196936, 1444743, 1732024, 2063321, 2443512, 2877823 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is also the number of 5-cycles in the (n+4)-path complement graph, - Eric W. Weisstein, Apr 11 2018

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Path Complement Graph

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = (n^5+5*n^3+4*n)/10.

G.f.: x*(1+2*x+6*x^2+2*x^3+x^4)/(1-x)^6. - Colin Barker, Jan 29 2012

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Eric W. Weisstein, Apr 11 2018

MATHEMATICA

Table[n (n^2 + 1) (n^2 + 4)/10, {n, 0, 20}] (* Eric W. Weisstein, Apr 11 2018 *)

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 8, 39, 136, 377, 888}, {0, 20}] (* Eric W. Weisstein, Apr 11 2018 *)

CoefficientList[Series[x (1 + 2 x + 6 x^2 + 2 x^3 + x^4)/(-1 + x)^6, {x, 0, 20}], x] (* Eric W. Weisstein, Apr 11 2018 *)

PROG

(PARI) { for (n=0, 1000, write("b060446.txt", n, " ", (n^5 + 5*n^3 + 4*n)/10); ) } \\ Harry J. Smith, Jul 05 2009

CROSSREFS

Cf. A054620.

Cf. A000292 (3-cycle count of \bar P_{n+4}), A002817 (4-cycle count of \bar P_{n+4}), A302695 (6-cycle count of \bar P_{n+5}).

Sequence in context: A200157 A101374 A163687 * A318267 A063002 A055581

Adjacent sequences:  A060443 A060444 A060445 * A060447 A060448 A060449

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 07 2001

STATUS

approved

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Last modified March 1 03:32 EST 2021. Contains 341732 sequences. (Running on oeis4.)