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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

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).

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).

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]

Crossrefs

Sequence in context: A247356 A291736 A010070 * A132445 A307437 A070846

Adjacent sequences: A291104 A291105 A291106 * A291108 A291109 A291110

Keyword

nonn

Author

Eric W. Weisstein, Aug 17 2017

Status

approved