A198310 Moore lower bound on the order of a (10,g)-cage.

11, 20, 101, 182, 911, 1640, 8201, 14762, 73811, 132860, 664301, 1195742, 5978711, 10761680, 53808401, 96855122, 484275611, 871696100, 4358480501, 7845264902, 39226324511, 70607384120, 353036920601, 635466457082, 3177332285411

Offset

3,1

Links

Paolo Xausa, Table of n, a(n) for n = 3..1000

Gordon Royle, Cages of higher valency

Index entries for linear recurrences with constant coefficients, signature (1,9,-9).

Formula

a(2i) = 2*Sum_{j=0..i-1} 9^j = string "2"^i read in base 9.

a(2i+1) = 9^i + 2*Sum_{j=0..i-1} 9^j = string "1"*"2"^i read in base 9.

From Colin Barker, Feb 01 2013: (Start)

a(n) = (-3-(-3)^n+4*3^n)/12.

a(n) = a(n-1)+9*a(n-2)-9*a(n-3).

G.f.: -x^3*(18*x^2-9*x-11) / ((x-1)*(3*x-1)*(3*x+1)). (End)

E.g.f.: (3*(cosh(3*x) - cosh(x) - sinh(x)) + 5*sinh(3*x))/12 - x - x^2. - Stefano Spezia, Apr 09 2022

Mathematica

A198310[n_] := (-3-(-3)^n+4*3^n)/12; Array[A198310, 30, 3] (* or *)
LinearRecurrence[{1, 9, -9}, {11, 20, 101}, 30] (* Paolo Xausa, Feb 21 2024 *)

Prog

(PARI) a(n)=(-3-(-3)^n+4*3^n)/12 \\ Charles R Greathouse IV, Jul 06 2017

Crossrefs

Moore lower bound on the order of a (k,g) cage: A198300 (square); rows: A000027 (k=2), A027383 (k=3), A062318 (k=4), A061547 (k=5), A198306 (k=6), A198307 (k=7), A198308 (k=8), A198309 (k=9), this sequence (k=10), A094626 (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), A188377 (g=7).

Sequence in context: A356986 A366207 A180113 * A085187 A061384 A071154

Adjacent sequences: A198307 A198308 A198309 * A198311 A198312 A198313

Keyword

nonn,easy,base

Author

Jason Kimberley, Oct 30 2011

Status

approved