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

1,1

Links

Table of n, a(n) for n=1..38.

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).

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)

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 *)

Crossrefs

Cf. A285272, A290587, A291053.

Sequence in context: A252591 A296849 A296380 * A104657 A000900 A124023

Adjacent sequences: A291050 A291051 A291052 * A291054 A291055 A291056

Keyword

nonn

Author

Eric W. Weisstein, Aug 17 2017

Extensions

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

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

Status

approved