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A307182 Crossing number of the n-crown graph (conjectured). 0
0, 0, 0, 0, 4, 12, 36, 72, 144, 240, 400, 600, 900, 1260, 1764, 2352, 3136, 4032, 5184, 6480, 8100, 9900, 12100, 14520, 17424, 20592, 24336, 28392, 33124, 38220, 44100, 50400, 57600, 65280, 73984, 83232, 93636, 104652, 116964, 129960, 144400, 159600, 176400, 194040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Sequence extended to n=1 and n=2 using the formula/recurrence.

LINKS

Table of n, a(n) for n=1..44.

Eric Weisstein's World of Mathematics, Crown Graph

Eric Weisstein's World of Mathematics, Graph Crossing Number

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

FORMULA

a(n)=(2*(n - 4)*n*(n^2 - 4*n + 5) - (2*n^2 - 8*n + 9) (-1)^n + 9)/32.

G.f.: -4*x^5*(1 + x + x^2)/((-1 + x)^5*(1 + x)^3).

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

MATHEMATICA

Table[(2 (n - 4) n (n^2 - 4 n + 5) - (2 n^2 - 8 n + 9) (-1)^n + 9)/32, {n, 20}]

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 0, 0, 4, 12, 36, 72}, 20]

CoefficientList[Series[-4 x^4 (1 + x + x^2)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A062858 A095735 A020875 * A190072 A063810 A183931

Adjacent sequences:  A307179 A307180 A307181 * A307183 A307184 A307185

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 28 2019

STATUS

approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)