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A051926 Number of independent sets of nodes in graph C_4 X P_n (n>2).

%I A051926 #37 Jul 02 2025 16:01:58
%S A051926 1,7,35,181,933,4811,24807,127913,659561,3400911,17536203,90422365,
%T A051926 466247117,2404121747,12396433487,63920042065,329592522065,
%U A051926 1699486218903,8763103574515,45185411569413,232990675202677,1201375684008283,6194683683674679,31941803427179001
%N A051926 Number of independent sets of nodes in graph C_4 X P_n (n>2).
%C A051926 Number of ways zero or more black and white stones can be placed on the points of a 2 X n grid such that no white stones are adjacent to any black stones. A078057 is a related case, where the grid is 1 X n. - _Wayne VanWeerthuizen_, May 04 2004
%H A051926 Vincenzo Librandi, <a href="/A051926/b051926.txt">Table of n, a(n) for n = 0..1000</a>
%H A051926 C. Bautista-Ramos and C. Guillen-Galvan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Bautista/bautista4.html">Fibonacci numbers of generalized Zykov sums</a>, J. Integer Seq., 15 (2012), Article 12.7.8.
%H A051926 Sela Fried and Toufik Mansour, <a href="https://arxiv.org/abs/2312.08273">Staircase graph words</a>, arXiv:2312.08273 [math.CO], 2023.
%H A051926 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,1,-1).
%F A051926 a(n) = 5*a(n-1)+a(n-2)-a(n-3) for n>2. - _Wayne VanWeerthuizen_, May 04 2004
%F A051926 G.f.: (1+2*x-x^2)/(1-5*x-x^2+x^3). - _Colin Barker_, Apr 18 2012
%t A051926 CoefficientList[Series[(1+2*x-x^2)/(1-5*x-x^2+x^3),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 27 2012 *)
%t A051926 LinearRecurrence[{5,1,-1},{1,7,35},40] (* _Harvey P. Dale_, Apr 29 2019 *)
%o A051926 (Magma) I:=[1, 7, 35]; [n le 3 select I[n] else 5*Self(n-1)+Self(n-2)-Self(n-3): n in [1..25]]; // _Vincenzo Librandi_, Apr 27 2012
%Y A051926 Row 4 of A286513.
%K A051926 easy,nonn
%O A051926 0,2
%A A051926 _Stephen G Penrice_, Dec 19 1999
%E A051926 More terms from _James Sellers_, Dec 20 1999