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

Author

Eric W. Weisstein, Aug 17 2017

Keywords

• nonn

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).

Crossrefs

Cf. A286954, A291107.

Programs

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]

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

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)

Extensions

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