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A198310 Moore lower bound on the order of a (10,g)-cage. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..27.

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.

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)). - Colin Barker, Feb 01 2013

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: A067969 A068599 A180113 * A085187 A061384 A071154

Adjacent sequences:  A198307 A198308 A198309 * A198311 A198312 A198313

KEYWORD

nonn,easy,base

AUTHOR

Jason Kimberley, Oct 30 2011

STATUS

approved

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Last modified January 22 16:36 EST 2018. Contains 298055 sequences.