login
a(n) = 2^n*(n/8 + 1) - n.
0

%I #6 Aug 17 2017 22:08:17

%S 3,8,20,47,106,233,504,1079,2294,4853,10228,21491,45042,94193,196592,

%T 409583,851950,1769453,3669996,7602155,15728618,32505833,67108840,

%U 138412007,285212646,587202533,1207959524,2483027939,5100273634,10468982753,21474836448,44023414751

%N a(n) = 2^n*(n/8 + 1) - n.

%C For n > 2, also the number of maximal irredundant sets in the n-helm graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HelmGraph.html">Helm Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).

%F a(n) = 2^n*(n/8 + 1) - n.

%F a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) -4*a(n-4).

%F G.f.: x^2*(3 - 10*x + 11*x^2 - 5*x^3)/(1 - 3*x + 2*x^2)^2.

%F E.g.f.: (1/4)*(1 + exp(x))*((4 +x)*exp(x) - (4 + 5*x)). - _G. C. Greubel_, Aug 17 2017

%t Table[2^n (n/8 + 1) - n, {n, 2, 20}]

%t LinearRecurrence[{6, -13, 12, -4}, {3, 8, 20, 47}, 20]

%t CoefficientList[Series[(3 - 10 x + 11 x^2 - 5 x^3)/(1 - 3 x + 2 x^2)^2, {x, 0, 20}], x]

%o (PARI) x='x+O('x^50); Vec(x^2*(3 - 10*x + 11*x^2 - 5*x^3)/(1 - 3*x + 2*x^2)^2) \\ _G. C. Greubel_, Aug 17 2017

%K nonn,easy

%O 2,1

%A _Eric W. Weisstein_, Aug 17 2017