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 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

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