OFFSET
1,2
COMMENTS
Sequence extended to n=1 using formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Vertex Cut
Eric Weisstein's World of Mathematics, Web Graph
Index entries for linear recurrences with constant coefficients, signature (20, -146, 480, -657, 60, 660, -400, -144, 128).
FORMULA
a(n) = 2^(3*n) - 1 - A286187(n). - Pontus von Brömssen, Apr 23 2023
a(n) = 20*a(n-1)-146*a(n-2)+480*a(n-3)-657*a(n-4)+60*a(n-5)+660*a(n-6)-400*a(n-7)-144*a(n-8)+128*a(n-9).
G.f.: x*(-1 - 10*x + 131*x^2 - 550*x^3 + 1008*x^4 - 628*x^5 + 128*x^6 - 448*x^7 + 384*x^8)/((-1 + 8*x)*(-1 + 6*x - 7*x^2 - 2*x^3 + 4*x^4)^2).
MATHEMATICA
LinearRecurrence[{20, -146, 480, -657, 60, 660, -400, -144, 128}, {1, 30, 323, 3110, 27777, 237498, 1977439, 16202990, 131490509}, 20]
CoefficientList[Series[(-1 - 10 x + 131 x^2 - 550 x^3 + 1008 x^4 - 628 x^5 + 128 x^6 - 448 x^7 + 384 x^8)/((-1 + 8 x) (-1 + 6 x - 7 x^2 - 2 x^3 + 4 x^4)^2), {x, 0, 20}], x]
With[{r = 4 + 2 # - 5 #^2 + #^3 &}, Table[8^n + n/2 - n RootSum[r, -494 #^n + 12 #1^(n + 1) + 35 #^(n + 2) &]/458 - RootSum[r, #^n &] - 1, {n, 20}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 23 2023
EXTENSIONS
More terms (based on data in A286187) from Pontus von Brömssen, Apr 23 2023
STATUS
approved