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%I #26 Sep 08 2022 08:45:53
%S 1,7,160,1390,19534,202528,2495596,27700276,326878816,3718923448,
%T 43234331704,496209443344,5738582748400,66066860825968,
%U 762649926287584,8789761525471360,101400012042254944,1169112414739169152,13483991218981408192,155487427811428691968
%N Expansion of (1-x+38*x^2-72*x^3-8*x^4+30*x^5) / (1-8*x -66*x^2 +280*x^3 +178*x^4 -532*x^5 -84*x^6 +108*x^7).
%H Robert Israel, <a href="/A177469/b177469.txt">Table of n, a(n) for n = 0..940</a>
%H S. Kitaev, A. Burstein and T. Mansour, <a href="http://www.ru.is/kennarar/sergey/index_files/Papers/burkitman_PUMA.pdf">Counting independent sets in certain classes of (almost) regular graphs</a>, Pure Mathematics and Applications (PU.M.A.) 19 (2008), no. 2-3, 17-26.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8, 66, -280, -178, 532, 84, -108).
%F G.f.: (1-x+38*x^2-72*x^3-8*x^4+30*x^5) / (1-8*x -66*x^2 +280*x^3 +178*x^4 -532*x^5 -84*x^6 +108*x^7).
%F a(0)=1, a(1)=7, a(2)=160, a(3)=1390, a(4)=19534, a(5)=202528, a(6)=2495596, a(n)=8*a(n-1) +66*a(n-2) -280*a(n-3) -178*a(n-4) +532*a(n-5)+ 84*a(n-6)-108*a(n-7). - _Harvey P. Dale_, Jul 04 2011
%p f:= gfun:-rectoproc({a(0)=1, a(1)=7, a(2)=160, a(3)=1390, a(4)=19534, a(5)=202528, a(6)=2495596, a(n)=8*a(n-1) +66*a(n-2) -280*a(n-3) -178*a(n-4) +532*a(n-5)+ 84*a(n-6)-108*a(n-7)},a(n),remember):
%p seq(f(n),n=0..30); # _Robert Israel_, Dec 21 2015
%t CoefficientList[Series[(1-x+38x^2-72x^3-8x^4+30x^5)/ (1-8x-66x^2+ 280x^3+ 178x^4- 532x^5- 84x^6+108x^7),{x,0,20}],x] (* or *) LinearRecurrence[ {8,66,-280,-178,532,84,-108}, {1,7,160,1390,19534,202528,2495596},21] (* _Harvey P. Dale_, Jul 04 2011 *)
%o (Magma) I:=[1,7,160,1390,19534,202528,2495596]; [n le 7 select I[n] else 8*Self(n-1)+66*Self(n-2)-280*Self(n-3)-178*Self(n-4)+532*Self(n-5)+84*Self(n-6)-108*Self(n-7): n in [1..30]]; // _Vincenzo Librandi_, Dec 22 2015
%K nonn
%O 0,2
%A Signy Olafsdottir (signy06(AT)ru.is), May 09 2010
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