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A198308 Moore lower bound on the order of an (8,g)-cage. 16
9, 16, 65, 114, 457, 800, 3201, 5602, 22409, 39216, 156865, 274514, 1098057, 1921600, 7686401, 13451202, 53804809, 94158416, 376633665, 659108914, 2636435657, 4613762400, 18455049601, 32296336802, 129185347209, 226074357616, 904297430465, 1582520503314 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Colin Barker, Table of n, a(n) for n = 3..1000

Gordon Royle, Cages of higher valency

Index entries for linear recurrences with constant coefficients, signature (1,7,-7).

FORMULA

a(2*i) = 2 Sum_{j=0..i-1} 7^j = string "2"^i read in base 7.

a(2*i+1) = 7^i + 2 Sum_{j=0..i-1} 7^j = string "1"*"2"^i read in base 7.

From Colin Barker, Feb 01 2013: (Start)

a(n) = a(n-1) + 7*a(n-2) - 7*a(n-3) for n>5.

G.f.: x^3*(9 + 7*x - 14*x^2) / ((1 - x)*(1 - 7*x^2)).

(End)

From Colin Barker, Mar 17 2017: (Start)

a(n) = (7^(n/2) - 1)/3 for n even.

a(n) = (4*7^(n/2-1/2) - 1)/3 for n odd.

(End)

PROG

(PARI) Vec(x^3*(9 + 7*x - 14*x^2) / ((1 - x)*(1 - 7*x^2)) + O(x^40)) \\ Colin Barker, Mar 17 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), this sequence (k=8), A198309 (k=9), A198310 (k=10), A094626 (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), A188377 (g=7).

Sequence in context: A119575 A174468 A203719 * A167349 A267763 A179307

Adjacent sequences:  A198305 A198306 A198307 * A198309 A198310 A198311

KEYWORD

nonn,easy,base

AUTHOR

Jason Kimberley, Oct 30 2011

STATUS

approved

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Last modified October 21 17:06 EDT 2018. Contains 316427 sequences. (Running on oeis4.)