login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198307 Moore lower bound on the order of a (7,g)-cage. 17
8, 14, 50, 86, 302, 518, 1814, 3110, 10886, 18662, 65318, 111974, 391910, 671846, 2351462, 4031078, 14108774, 24186470, 84652646, 145118822, 507915878, 870712934, 3047495270, 5224277606, 18284971622, 31345665638, 109709829734, 188073993830, 658258978406 (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 (1,6,-6).

FORMULA

a(2*i) = 2 sum_{j=0}^{i-1}6^j =  string "2"^i read in base 6.

a(2*i+1) = 6^i +  2 sum_{j=0}^{i-1}6^j = string "1"*"2"^i read in base 6.

a(n) <= A218555(n).

From Colin Barker, Feb 01 2013: (Start)

a(n) = a(n-1) + 6*a(n-2) - 6*a(n-3) for n>5.

G.f.: 2*x^3*(4 + 3*x - 6*x^2) / ((1 - x)*(1 - 6*x^2)).

(End)

From Colin Barker, Mar 17 2017: (Start)

a(n) = 2*(6^(n/2) - 1)/5 for n>2 and even.

a(n) = (7*6^(n/2-1/2) - 2)/5 for n>2 and odd.

(End)

MATHEMATICA

DeleteCases[CoefficientList[Series[2 x^3*(4 + 3 x - 6 x^2)/((1 - x) (1 - 6 x^2)), {x, 0, 31}], x], 0] (* Michael De Vlieger, Mar 17 2017 *)

LinearRecurrence[{1, 6, -6}, {8, 14, 50}, 30] (* or *) CoefficientList[ Series[ -((2 (-4-3 x+6 x^2))/(1-x-6 x^2+6 x^3)), {x, 0, 30}], x] (* Harvey P. Dale, Aug 03 2021 *)

PROG

(PARI) Vec(2*x^3*(4 + 3*x - 6*x^2) / ((1 - x)*(1 - 6*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), this sequence (k=7), A198308 (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: A111050 A009453 A332658 * A218555 A268160 A236553

Adjacent sequences:  A198304 A198305 A198306 * A198308 A198309 A198310

KEYWORD

nonn,easy,base

AUTHOR

Jason Kimberley, Oct 30 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 21:59 EST 2021. Contains 349596 sequences. (Running on oeis4.)