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
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 28 2019
STATUS
approved