A291537 a(n) = 8^n - 3*2^n + 5.

7, 57, 493, 4053, 32677, 261957, 2096773, 16776453, 134216197, 1073738757, 8589928453, 68719464453, 549755789317, 4398046461957, 35184371990533, 281474976514053, 2251799813292037, 18014398508695557, 144115188074283013, 1152921504603701253, 9223372036848484357

Offset: 1

Author

Eric W. Weisstein, Aug 25 2017

Keywords

• nonn
• easy

Comments

Number of dominating sets in the n X n X n complete tripartite graph.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph
• Eric Weisstein's World of Mathematics, Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (11,-26,16).

Programs

Mathematica

Table[8^n - 3 2^n + 5, {n, 20}]
LinearRecurrence[{11, -26, 16}, {7, 57, 493}, 20]
CoefficientList[Series[(-7 + 20 x - 48 x^2)/(-1 + 11 x - 26 x^2 + 16 x^3), {x, 0, 20}], x]

PARI

x='x+O('x^50); Vec(x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3)) \\ G. C. Greubel, Aug 26 2017

Formula

a(n) = 8^n - 3*2^n + 5.

a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3).

G.f.: x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3).

E.g.f.: exp(8*x) - 3*exp(2*x) + 5*exp(x) - 3. - G. C. Greubel, Aug 26 2017