OFFSET
1,1
COMMENTS
The only disconnected induced subgraphs are those constructed from the vertices of a single partition. - Andrew Howroyd, Aug 10 2017
LINKS
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (12, -37, 42, -16).
FORMULA
a(n) = 8^n - 3*2^n + 3*n + 2. - Andrew Howroyd, Aug 10 2017
a(n) = 12*a(n-1) - 37*a(n-2) + 42*a(n-3) - 16*a(n-4).
G.f.: (x (7 - 24 x + 38 x^2))/((-1 + x)^2 (1 - 10 x + 16 x^2)).
MATHEMATICA
Table[8^n - 3 2^n + 3 n + 2, {n, 20}]
LinearRecurrence[{12, -37, 42, -16}, {7, 60, 499, 4062}, 20]
CoefficientList[Series[(7 - 24 x + 38 x^2)/((-1 + x)^2 (1 - 10 x + 16 x^2)), {x, 0, 20}], x]
PROG
(PARI) a(n) = 8^n - 3*2^n + 3*n + 2; \\ Andrew Howroyd, Aug 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 09 2017
EXTENSIONS
a(7)-a(20) from Andrew Howroyd, Aug 10 2017
STATUS
approved