A290513 Number of irredundant sets in the n-ladder graph.

3, 11, 26, 79, 224, 640, 1828, 5225, 14928, 42654, 121873, 348232, 995003, 2843014, 8123337, 23210809, 66320216, 189496620, 541448364, 1547079580, 4420468031, 12630596045, 36089381477, 103118131368, 294639269914, 841872308017, 2405480380385, 6873175192304

Offset

1,1

Comments

Row 2 of A286868.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Irredundant Set

Eric Weisstein's World of Mathematics, Ladder Graph

Index entries for linear recurrences with constant coefficients, signature (2, 1, 3, 5, -2, -6, -5, -4, -4, -3, -2, -2).

Formula

From Andrew Howroyd, Aug 04 2017: (Start)

a(n) = 2*a(n-1) + a(n-2) + 3*a(n-3) + 5*a(n-4) - 2*a(n-5) - 6*a(n-6) - 5*a(n-7) - 4*a(n-8) - 4*a(n-9) - 3*a(n-10) - 2*a(n-11) - 2*a(n-12).

G.f.: x*(3 + 5*x + x^2 + 7*x^3 - 8*x^4 - 14*x^5 - 3*x^6 - 5*x^7 - 9*x^8 - 3*x^9 - 2*x^10 - 2*x^11) / (1 - 2*x - x^2 - 3*x^3 - 5*x^4 + 2*x^5 + 6*x^6 + 5*x^7 + 4*x^8 + 4*x^9 + 3*x^10 + 2*x^11 + 2*x^12).

(End)

Mathematica

Table[RootSum[2 + 2 # + 3 #^2 + 4 #^3 + 4 #^4 + 5 #^5 + 6 #^6 + 2 #^7 - 5 #^8 - 3 #^9 - #^10 - 2 #^11 + #^12 &, -105577159431355949 #^n - 389671420034091247 #^(n + 1) + 29241021604101932 #^(n + 2) + 551171239538727862 #^(n + 3) - 835076245333578054 #^(n + 4) - 823168743731791895 #^(n + 5) + 1288188291747539683 #^(n + 6) + 114497498217658607 #^(n + 7) - 529545500369064866 #^(n + 8) + 763912087212707104 #^(n + 9) - 593709228550713556 #^(n + 10) + 130400048784652699 #^(n + 11) &]/2485579507903393779, {n, 20}] (* Eric W. Weisstein, Aug 05 2017 *)
LinearRecurrence[{2, 1, 3, 5, -2, -6, -5, -4, -4, -3, -2, -2}, {3, 11, 26, 79, 224, 640, 1828, 5225, 14928, 42654, 121873, 348232}, 20] (* Eric W. Weisstein, Aug 05 2017 *)
CoefficientList[Series[(3 + 5 x + x^2 + 7 x^3 - 8 x^4 - 14 x^5 - 3 x^6 - 5 x^7 - 9 x^8 - 3 x^9 - 2 x^10 - 2 x^11)/(1 - 2 x - x^2 - 3 x^3 - 5 x^4 + 2 x^5 + 6 x^6 + 5 x^7 + 4 x^8 + 4 x^9 + 3 x^10 + 2 x^11 + 2 x^12), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 05 2017 *)

Prog

(PARI) Vec((3+5*x+x^2+7*x^3-8*x^4-14*x^5-3*x^6-5*x^7-9*x^8-3*x^9-2*x^10-2*x^11)/(1-2*x-x^2-3*x^3-5*x^4+2*x^5+6*x^6+5*x^7+4*x^8+4*x^9+3*x^10+2*x^11+2*x^12)+O(x^30)) \\ Andrew Howroyd, Aug 04 2017

Crossrefs

Cf. A286868 (irredundant sets in m X n grid graph).

Sequence in context: A011942 A220147 A256315 * A101612 A123928 A186301

Adjacent sequences: A290510 A290511 A290512 * A290514 A290515 A290516

Keyword

nonn

Author

Eric W. Weisstein, Aug 04 2017

Extensions

Terms a(11) and beyond from Andrew Howroyd, Aug 04 2017

Status

approved