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%I #28 Feb 21 2024 08:18:16
%S 11,20,101,182,911,1640,8201,14762,73811,132860,664301,1195742,
%T 5978711,10761680,53808401,96855122,484275611,871696100,4358480501,
%U 7845264902,39226324511,70607384120,353036920601,635466457082,3177332285411
%N Moore lower bound on the order of a (10,g)-cage.
%H Paolo Xausa, <a href="/A198310/b198310.txt">Table of n, a(n) for n = 3..1000</a>
%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cages/allcages.html">Cages of higher valency</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,-9).
%F a(2i) = 2*Sum_{j=0..i-1} 9^j = string "2"^i read in base 9.
%F a(2i+1) = 9^i + 2*Sum_{j=0..i-1} 9^j = string "1"*"2"^i read in base 9.
%F From _Colin Barker_, Feb 01 2013: (Start)
%F a(n) = (-3-(-3)^n+4*3^n)/12.
%F a(n) = a(n-1)+9*a(n-2)-9*a(n-3).
%F G.f.: -x^3*(18*x^2-9*x-11) / ((x-1)*(3*x-1)*(3*x+1)). (End)
%F E.g.f.: (3*(cosh(3*x) - cosh(x) - sinh(x)) + 5*sinh(3*x))/12 - x - x^2. - _Stefano Spezia_, Apr 09 2022
%t A198310[n_] := (-3-(-3)^n+4*3^n)/12; Array[A198310, 30, 3] (* or *)
%t LinearRecurrence[{1, 9, -9}, {11, 20, 101}, 30] (* _Paolo Xausa_, Feb 21 2024 *)
%o (PARI) a(n)=(-3-(-3)^n+4*3^n)/12 \\ _Charles R Greathouse IV_, Jul 06 2017
%Y 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).
%K nonn,easy,base
%O 3,1
%A _Jason Kimberley_, Oct 30 2011
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