A291102 Number of maximal irredundant sets in the n-pan graph.

2, 2, 3, 7, 9, 13, 19, 24, 39, 63, 87, 124, 183, 272, 405, 593, 867, 1261, 1869, 2760, 4046, 5936, 8712, 12817, 18861, 27720, 40711, 59792, 87915, 129250, 189946, 279118, 410135, 602803, 886008, 1302157, 1913622, 2812220, 4133091, 6074385, 8927330, 13119959

Offset

1,1

Comments

Sequence extended to a(1)-a(2) using the formula/recurrence. - Andrew Howroyd, Aug 23 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Maximal Irredundant Set

Eric Weisstein's World of Mathematics, Pan Graph

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 1, 0, -1, -2, -1, 2, 1, 0, 0, -1).

Formula

From Andrew Howroyd, Aug 23 2017: (Start)

a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) - a(n-7) - 2*a(n-8) - a(n-9) + 2*a(n-10) + a(n-11) - a(n-14) for n > 14.

G.f.: x*(2 + 2*x + x^2 + 3*x^3 + 2*x^4 - x^5 - 2*x^6 - 6*x^7 - 3*x^8 + 7*x^9 + 3*x^10 - x^11 - 4*x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14).

(End)

Mathematica

Table[-RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, 500851004670498 #^(n+1) - 3689002954543242 #^(n+2) - 4674357321032747 #^(n+3) - 11682114439256677 #^(n+4) + 4235991226348286 #^(n+5) + 7038537508218316 #^(n+6) + 7181640141870472 #^(n+7) + 1546373234795414 #^(n+8) - 8648457478830123 #^(n+9) - 8135065519248445 #^(n+10) - 4540890555566032 #^(n+11) - 5314826024895471 #^(n+12) - 1546564184442276 #^(n+13) + 6933486092556085 #^(n+14) &]/47617929706047629, {n, 20}]
LinearRecurrence[{0, 1, 1, 1, 1, 0, -1, -2, -1, 2, 1, 0, 0, -1}, {2, 2, 3, 7, 9, 13, 19, 24, 39, 63, 87, 124, 183, 272}, 20]
CoefficientList[Series[(2 + 2 x + x^2 + 3 x^3 + 2 x^4 - x^5 - 2 x^6 - 6 x^7 - 3 x^8 + 7 x^9 + 3 x^10 - x^11 - 4 x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2 x^8 + x^9 - 2 x^10 - x^11 + x^14), {x, 0, 20}], x]

Prog

(PARI) Vec((2 + 2*x + x^2 + 3*x^3 + 2*x^4 - x^5 - 2*x^6 - 6*x^7 - 3*x^8 + 7*x^9 + 3*x^10 - x^11 - 4*x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14)+O(x^40)) \\ Andrew Howroyd, Aug 23 2017

Crossrefs

Cf. A286954, A291107.

Sequence in context: A160433 A043550 A237988 * A208494 A036060 A227300

Adjacent sequences: A291099 A291100 A291101 * A291103 A291104 A291105

Keyword

nonn

Author

Eric W. Weisstein, Aug 17 2017

Extensions

a(1)-a(2) and terms a(21) and beyond from Andrew Howroyd, Aug 23 2017

Status

approved