A291053 Number of maximal irredundant sets in the n-Andrásfai graph.

2, 10, 28, 88, 217, 493, 989, 1794, 3016, 4785, 7256, 10612, 15067, 20869, 28303, 37694, 49410, 63865, 81522, 102896, 128557, 159133, 195313, 237850, 287564, 345345, 412156, 489036, 577103, 677557, 791683, 920854, 1066534, 1230281, 1413750, 1618696, 1846977, 2100557

Offset: 1

Author

Eric W. Weisstein, Aug 17 2017

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Andrásfai Graph
• Eric Weisstein's World of Mathematics, Maximal Irredundant Set
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A285272, A290587, A291053.

Programs

Mathematica

Table[Piecewise[{{2, n == 1}, {10, n == 2}, {28, n == 3}}, (-3120 + 10932 n - 4970 n^2 + 765 n^3 - 10 n^4 + 3 n^5)/120], {n, 20}]
Join[{2, 10, 28}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {88, 217, 493, 989, 1794, 3016}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[(2 - 2 x - 2 x^2 + 30 x^3 - 61 x^4 + 89 x^5 - 112 x^6 + 77 x^7 - 18 x^8)/(-1 + x)^6, {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

Formula

From Eric W. Weisstein, Aug 21 2017: (Start)

a(n) = (-3120 + 10932*n - 4970*n^2 + 765*n^3 - 10*n^4 + 3*n^5)/120 for n > 3.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 9.

G.f.: (x (2 - 2 x - 2 x^2 + 30 x^3 - 61 x^4 + 89 x^5 - 112 x^6 + 77 x^7 - 18 x^8))/(-1 + x)^6.

(End)

Extensions

a(9)-a(20) from Andrew Howroyd, Aug 19 2017

a(21) and above from Eric W. Weisstein, Aug 21 2017