A289121 a(n) = (8 - 2*n + 11*n^2 - 6*n^3 + n^4)/4.

3, 4, 5, 12, 37, 98, 219, 430, 767, 1272, 1993, 2984, 4305, 6022, 8207, 10938, 14299, 18380, 23277, 29092, 35933, 43914, 53155, 63782, 75927, 89728, 105329, 122880, 142537, 164462, 188823, 215794, 245555, 278292, 314197, 353468, 396309, 442930, 493547, 548382, 607663

Offset: 1

Author

Eric W. Weisstein, Aug 17 2017

Keywords

• nonn
• easy

Comments

For n > 1, number of maximal irredundant sets in the n-crown graph.

Links

• Eric Weisstein's World of Mathematics, Crown Graph
• Eric Weisstein's World of Mathematics, Maximal Irredundant Set
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Magma

[(8 - 2*n + 11*n^2 - 6*n^3 + n^4)/4 : n in [1..50]]; // Wesley Ivan Hurt, Dec 02 2021

Mathematica

Table[(8 - 2 n + 11 n^2 - 6 n^3 + n^4)/4, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {3, 4, 5, 12, 37}, 20]
CoefficientList[Series[(-3 + 11 x - 15 x^2 + 3 x^3 - 2 x^4)/(-1 + x)^5, {x, 0, 20}], x]

PARI

x='x+O('x^50); Vec(x*(3 - 11*x + 15*x^2 - 3*x^3 + 2*x^4)/(1 - x)^5) \\ G. C. Greubel, Aug 17 2017

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: x*(3 - 11*x + 15*x^2 - 3*x^3 + 2*x^4)/(1 - x)^5.

E.g.f.: (1/4)*((8 + 4*x + x^4)*exp(x) - 8). - G. C. Greubel, Aug 17 2017