OFFSET
2,1
LINKS
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, White Bishop Graph
Index entries for linear recurrences with constant coefficients, signature (2, 4, -10, 1, 8, -4).
FORMULA
a(n) = ((-1)^(n + 1) + 2^(n + 1)*(17 + (-1)^n) - 6*n*(n + 4) - 23)/12.
a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) + a(n-4) + 8*a(n-5) - 4*a(n-6).
G.f.: x^2*(4 + x - 4*x^2 + 5*x^3 + 4*x^4 - 4*x^5)/((-1 + x)^3*(-1 - x + 4*x^2 + 4*x^3)).
MATHEMATICA
Table[((-1)^(n + 1) + 2^(n + 1) (17 + (-1)^n) - 6 n (n + 4) - 23)/12, {n, 20}]
LinearRecurrence[{2, 4, -10, 1, 8, -4}, {4, 9, 30, 61, 160, 301}, 20]
Rest @ CoefficientList[Series[x (4 + x - 4 x^2 + 5 x^3 + 4 x^4 - 4 x^5)/((-1 + x)^3 (-1 - x + 4 x^2 + 4 x^3)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 29 2017
STATUS
approved