A290756 Number of (non-null) connected induced subgraphs of the complete tripartite graph K_{n,n,n}.

7, 60, 499, 4062, 32689, 261972, 2096791, 16776474, 134216221, 1073738784, 8589928483, 68719464486, 549755789353, 4398046461996, 35184371990575, 281474976514098, 2251799813292085, 18014398508695608, 144115188074283067, 1152921504603701310

Offset: 1

Author

Eric W. Weisstein, Aug 09 2017

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A286191.

Programs

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]

PARI

a(n) = 8^n - 3*2^n + 3*n + 2; \\ Andrew Howroyd, Aug 10 2017

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)).

Extensions

a(7)-a(20) from Andrew Howroyd, Aug 10 2017