OFFSET
1,2
COMMENTS
Sequence extended to n = 1 using formula.
LINKS
Eric Weisstein's World of Mathematics, Prism Graph
Eric Weisstein's World of Mathematics, Vertex Cut
Index entries for linear recurrences with constant coefficients, signature (10,-35,48,-11,-22,7,4).
FORMULA
a(n) = 2^(2*n) - A286182(n) - 1. - Pontus von Brömssen, Aug 30 2022
From Eric W. Weisstein, Aug 31 2022: (Start)
a(n) = 4^n + 3*n - 3*n*Fibonacci(n, 2) - Lucas(n, 2), where Fibonacci(n, 2) = A000129(n) and Lucas(n, 2) = A002203(n).
a(n) = 10*a(n-1) - 35*a(n-2) + 48*a(n-3) - 11*a(n-4) - 22*a(n-5) + 7*a(n-6) + 4*a(n-7).
G.f.: 2*x^2*(-1 + 4*x - 19*x^2 + 18*x^3 + 10*x^4 + 6*x^5)/((-1 + x)^2*(-1 + 4*x)*(-1 + 2*x + x^2)^2). (End)
MATHEMATICA
Table[4^n + 3 n - 3 n Fibonacci[n, 2] - LucasL[n, 2] - 2, {n, 20}]
LinearRecurrence[{10, -35, 48, -11, -22, 7, 4}, {0, 2, 12, 88, 520, 2654, 12376}, 20]
CoefficientList[Series[2 x (-1 + 4 x - 19 x^2 + 18 x^3 + 10 x^4 + 6 x^5)/((-1 + x)^2 (-1 + 4 x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 30 2022
EXTENSIONS
More terms from Pontus von Brömssen, Aug 30 2022
STATUS
approved