cp's OEIS Frontend

A050400 Number of independent sets of vertices in P_3 X C_n (n > 2).

%I A050400 #21 Sep 13 2023 11:15:52
%S A050400 5,1,17,43,181,621,2309,8303,30277,109753,398857,1447931,5258725,
%T A050400 19095285,69344061,251811903,914429445,3320635025,12058502657,
%U A050400 43789003563,159014593621,577442573597,2096914206261,7614694850543,27651860345029,100414447219721,364643142303353
%N A050400 Number of independent sets of vertices in P_3 X C_n (n > 2).
%H A050400 Vincenzo Librandi, <a href="/A050400/b050400.txt">Table of n, a(n) for n = 0..1000</a>
%H A050400 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,8,6,-1,-1).
%F A050400 a(n) = a(n-1) + 8*a(n-2) + 6*a(n-3) - a(n-4) - a(n-5).
%F A050400 G.f.: (5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
%p A050400 seq(coeff(series((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Oct 30 2019
%t A050400 CoefficientList[Series[(5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+ x^4)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 11 2017 *)
%o A050400 (Magma) I:=[5,1,17,43,181]; [n le 5 select I[n] else Self(n-1) + 8*Self(n-2) + 6*Self(n-3) - Self(n-4) - Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, May 11 2017
%o A050400 (PARI) my(x='x+O('x^30)); Vec((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))) \\ _G. C. Greubel_, Oct 30 2019
%o A050400 (Sage)
%o A050400 def A077952_list(prec):
%o A050400     P.<x> = PowerSeriesRing(ZZ, prec)
%o A050400     return P((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))).list()
%o A050400 A077952_list(30) # _G. C. Greubel_, Oct 30 2019
%o A050400 (GAP) a:=[5,1,17,43,181];; for n in [6..30] do a[n]:=a[n-1]+8*a[n-2] +6*a[n-3] -a[n-4]-a[n-5]; od; a; # _G. C. Greubel_, Oct 30 2019
%Y A050400 Column 3 of A286513.
%K A050400 easy,nonn
%O A050400 0,1
%A A050400 _Stephen G Penrice_, Dec 21 1999
%E A050400 More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999