OFFSET
1,2
COMMENTS
Sequence extended to n = 1 using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Helm Graph
Eric Weisstein's World of Mathematics, Vertex Cut
Index entries for linear recurrences with constant coefficients, signature (13, -67, 175, -244, 172, -48).
FORMULA
a(n) = 2^(2*n+1) - 1 - A286184(n). - Pontus von Brömssen, Apr 23 2023
a(n) = (2^n - 1)*(1 + 2^(n + 1) - n) - 3^n.
a(n) = 13*a(n-1)-67*a(n-2)+175*a(n-3)-244*a(n-4)+172*a(n-5)-48*a(n-6).
G.f.: x*(1 - x - 18*x^2 + 60*x^3 - 84*x^4 + 48*x^5)/((-1 + x)^2*(-1 + 2*x)^2*(-1 + 3*x)*(-1 + 4*x)).
MATHEMATICA
Table[(2^n - 1) (1 + 2^(n + 1) - n) - 3^n, {n, 20}]
LinearRecurrence[{13, -67, 175, -244, 172, -48}, {1, 12, 71, 354, 1617, 7020}, 20]
CoefficientList[Series[(1 - x - 18 x^2 + 60 x^3 - 84 x^4 + 48 x^5)/((-1 + x)^2 (-1 + 2 x)^2 (-1 + 3 x) (-1 + 4 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 23 2023
EXTENSIONS
More terms (based on data in A286184) from Pontus von Brömssen, Apr 23 2023
STATUS
approved