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%I #15 Sep 08 2022 08:45:10
%S 1,3,5,9,14,18,26,34,41,52,64,72,87,102,113,131,150,162,184,206,221,
%T 246,272,288,317,346,365,397,430,450,486,522,545,584,624,648,691,734,
%U 761,807,854,882,932,982,1013,1066,1120,1152,1209,1266
%N Independence number of king KG_4 on triangle board B_n.
%H J.-J. Bode, H. Harborth and M. Harborth, <a href="http://dx.doi.org/10.1016/S0012-365X(02)00825-7">King independence on triangle boards</a>, Discr. Math., 266 (2003), 101-107.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,1,-1,0,-1,1).
%F a(n)= a(n-1) +a(n-3) -a(n-4) +a(n-6) -a(n-7) -a(n-9) +a(n-10), n>12.
%F G.f.: x*(x^11 -x^10 -x^8 -x^7 -3*x^6 -2*x^5 -3*x^4 -3*x^3 -2*x^2 -2*x -1) / ((x -1)^3*(x +1)*(x^2 -x +1)*(x^2 +x +1)^2). - _Colin Barker_, Aug 06 2014
%p A082874 := proc(n)
%p if n = 1 then
%p 1;
%p elif n = 2 then
%p 3;
%p else
%p m := modp(n,6) ;
%p 3*n^2+op(m+1,[0,n+2,2*n-4,3,n+2,2*n-1]) ;
%p %/6 ;
%p end if ;
%p end proc:
%p seq(A082874(n),n=1..50) ; # _R. J. Mathar_, Aug 05 2014
%o (Magma) I:=[1,3,5,9,14,18,26,34,41,52,64,72]; [n le 12 select I[n] else Self(n-1)+Self(n-3)-Self(n-4)+Self(n-6)-Self(n-7)-Self(n-9)+Self(n-10): n in [1..60]]; // _Vincenzo Librandi_, Aug 06 2014
%o (PARI) Vec(x*(x^11-x^10-x^8-x^7-3*x^6-2*x^5-3*x^4-3*x^3-2*x^2-2*x-1)/((x-1)^3*(x+1)*(x^2-x+1)*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Aug 06 2014
%Y Cf. A082873.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, May 25 2003
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