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 A198306 Moore lower bound on the order of a (6,g)-cage. 16
 7, 12, 37, 62, 187, 312, 937, 1562, 4687, 7812, 23437, 39062, 117187, 195312, 585937, 976562, 2929687, 4882812, 14648437, 24414062, 73242187, 122070312, 366210937, 610351562, 1831054687, 3051757812, 9155273437, 15258789062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Gordon Royle, Cages of higher valency Index entries for linear recurrences with constant coefficients, signature (1,5,-5). FORMULA a(2*i) = 2 sum_{j=0}^{i-1}5^j =  string "2"^i read in base 5. a(2*i+1) = 5^i +  2 sum_{j=0}^{i-1}5^j = string "1"*"2"^i read in base 5. a(n) <= A218554(n). - Jason Kimberley, Dec 21 2012 a(n) = a(n-1)+5*a(n-2)-5*a(n-3). G.f.: -x^3*(10*x^2-5*x-7) / ((x-1)*(5*x^2-1)). - Colin Barker, Feb 01 2013 From Colin Barker, Nov 25 2016: (Start) a(n) = (5^(n/2) - 1)/2 for n>2 and even. a(n) = (3*5^((n-1)/2) - 1)/2 for n>2 and odd. (End) MATHEMATICA LinearRecurrence[{1, 5, -5}, {7, 12, 37}, 30] (* Harvey P. Dale, Jun 28 2015 *) 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), this sequence (k=6), A198307 (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: A078575 A220036 A197229 * A218554 A113499 A178681 Adjacent sequences:  A198303 A198304 A198305 * A198307 A198308 A198309 KEYWORD nonn,easy,base AUTHOR Jason Kimberley, Oct 30 2011 STATUS approved

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