A291097 a(n) = 2^n*(n/8 + 1) - n.

3, 8, 20, 47, 106, 233, 504, 1079, 2294, 4853, 10228, 21491, 45042, 94193, 196592, 409583, 851950, 1769453, 3669996, 7602155, 15728618, 32505833, 67108840, 138412007, 285212646, 587202533, 1207959524, 2483027939, 5100273634, 10468982753, 21474836448, 44023414751

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..33.

Eric Weisstein's World of Mathematics, Helm Graph

Eric Weisstein's World of Mathematics, Maximal Irredundant Set

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Formula

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

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

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

E.g.f.: (1/4)*(1 + exp(x))*((4 +x)*exp(x) - (4 + 5*x)). - G. C. Greubel, Aug 17 2017

Mathematica

Table[2^n (n/8 + 1) - n, {n, 2, 20}]
LinearRecurrence[{6, -13, 12, -4}, {3, 8, 20, 47}, 20]
CoefficientList[Series[(3 - 10 x + 11 x^2 - 5 x^3)/(1 - 3 x + 2 x^2)^2, {x, 0, 20}], x]

Prog

(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

Crossrefs

Sequence in context: A138803 A048492 A006776 * A293883 A050231 A136305

Adjacent sequences: A291094 A291095 A291096 * A291098 A291099 A291100

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 17 2017

Status

approved