A291107 Number of irredundant sets in the n-pan graph.

3, 5, 7, 16, 26, 42, 72, 125, 216, 367, 629, 1079, 1852, 3173, 5438, 9323, 15984, 27401, 46971, 80522, 138039, 236639, 405665, 695425, 1192158, 2043700, 3503484, 6005970, 10295947, 17650192, 30257465, 51869927, 88919855, 152434004, 261315377, 447969116, 767946883

Offset: 1

Author

Eric W. Weisstein, Aug 17 2017

Keywords

• nonn

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

• Eric Weisstein's World of Mathematics, Irredundant Set
• Eric Weisstein's World of Mathematics, Pan Graph
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 1, 0, -1).

Programs

Mathematica

Table[RootSum[1 - #^2 - #^4 - #^5 + #^6 &, 59603 #^n - 12384 #^(1 + n) - 10700 #^(2 + n) + 17668 #^(3 + n) + 3457 #^(4 + n) + 1652 #^(5 + n) &]/89653, {n, 20}]
LinearRecurrence[{1, 1, 0, 1, 0, -1}, {3, 5, 7, 16, 26, 42, 72, 125}, 20]
CoefficientList[Series[(3 + 2 x - x^2 + 4 x^3 - 5 x^5)/(1 - x - x^2 - x^4 + x^6), {x, 0, 20}], x]

Formula

a(n) = a(n-1) + a(n-2) + a(n-4) - a(n-6).

G.f.: (x (3 + 2 x - x^2 + 4 x^3 - 5 x^5))/(1 - x - x^2 - x^4 + x^6).