OFFSET
3,1
LINKS
Paolo Xausa, Table of n, a(n) for n = 3..1000
Gordon Royle, Cages of higher valency
Index entries for linear recurrences with constant coefficients, signature (1,9,-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.
From Colin Barker, Feb 01 2013: (Start)
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)). (End)
E.g.f.: (3*(cosh(3*x) - cosh(x) - sinh(x)) + 5*sinh(3*x))/12 - x - x^2. - Stefano Spezia, Apr 09 2022
MATHEMATICA
LinearRecurrence[{1, 9, -9}, {11, 20, 101}, 30] (* Paolo Xausa, Feb 21 2024 *)
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).
KEYWORD
nonn,easy,base
AUTHOR
Jason Kimberley, Oct 30 2011
STATUS
approved