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%I A121800 #10 Jul 31 2015 20:35:36 %S A121800 0,159,4694,36506,190224,1152620,6013304,33863688,180138368,989566320, %T A121800 5317362784,28948792992,156246056704,847762543808,4584148419456, %U A121800 24840385901696,134422525407232,728032988040960,3940920763725312 %N A121800 a(n)= 4*a(n-1) +18*a(n-2) -48*a(n-3) -60*a(n-4) +80*a(n-5) +56*a(n-6). %C A121800 As indicated by the generating function, this can be written as a linear combination of A007070, A081180 and A000079. [Oct 14 2009] %H A121800 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, 18, -48, -60, 80, 56). %F A121800 G.f.: x^2*(-159-4058*x-14868*x^2+32660*x^3+30532*x^4)/( (2*x^2-1) * (2*x^2+4*x+1) * ( 14*x^2-8*x+1)). [Oct 14 2009] %t A121800 M = {{0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}}; v[1] = Table[Fibonacci[n], {n, 0, 17}] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}] %t A121800 LinearRecurrence[{4,18,-48,-60,80,56},{0,159,4694,36506,190224,1152620},40] (* _Harvey P. Dale_, May 13 2012 *) %K A121800 nonn %O A121800 1,2 %A A121800 _Roger L. Bagula_, Aug 27 2006 %E A121800 Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009