cp's OEIS Frontend

A198308 Moore lower bound on the order of an (8,g)-cage.

%I A198308 #27 Apr 09 2022 17:39:09
%S A198308 9,16,65,114,457,800,3201,5602,22409,39216,156865,274514,1098057,
%T A198308 1921600,7686401,13451202,53804809,94158416,376633665,659108914,
%U A198308 2636435657,4613762400,18455049601,32296336802,129185347209,226074357616,904297430465,1582520503314
%N A198308 Moore lower bound on the order of an (8,g)-cage.
%H A198308 Colin Barker, <a href="/A198308/b198308.txt">Table of n, a(n) for n = 3..1000</a>
%H A198308 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cages/allcages.html">Cages of higher valency</a>
%H A198308 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,7,-7).
%F A198308 a(2*i) = 2 Sum_{j=0..i-1} 7^j = string "2"^i read in base 7.
%F A198308 a(2*i+1) = 7^i + 2 Sum_{j=0..i-1} 7^j = string "1"*"2"^i read in base 7.
%F A198308 From _Colin Barker_, Feb 01 2013: (Start)
%F A198308 a(n) = a(n-1) + 7*a(n-2) - 7*a(n-3) for n>5.
%F A198308 G.f.: x^3*(9 + 7*x - 14*x^2) / ((1 - x)*(1 - 7*x^2)). (End)
%F A198308 From _Colin Barker_, Mar 17 2017: (Start)
%F A198308 a(n) = (7^(n/2) - 1)/3 for n even.
%F A198308 a(n) = (4*7^(n/2-1/2) - 1)/3 for n odd. (End)
%F A198308 E.g.f.: (7*(cosh(sqrt(7)*x) - cosh(x) - sinh(x)) + 4*sqrt(7)*sinh(sqrt(7)*x) - 21*x*(1 + x))/21. - _Stefano Spezia_, Apr 09 2022
%t A198308 LinearRecurrence[{1,7,-7},{9,16,65},40] (* _Harvey P. Dale_, Oct 14 2019 *)
%o A198308 (PARI) Vec(x^3*(9 + 7*x - 14*x^2) / ((1 - x)*(1 - 7*x^2)) + O(x^40)) \\ _Colin Barker_, Mar 17 2017
%Y A198308 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).
%K A198308 nonn,easy,base
%O A198308 3,1
%A A198308 _Jason Kimberley_, Oct 30 2011