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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
OFFSET
1,5
COMMENTS
Sequence extended to n=1 and n=2 using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Graph Crossing Number
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 * A374906 A357061 A190072
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 28 2019
STATUS
approved