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%I #18 Jul 18 2020 10:04:49
%S 1,2,6,8,13,18,25,32,41,50,61,72,85,98,113,128,145,162,181,200,221,
%T 242,265,288,313,338,365,392,421,450,481,512,545,578,613,648,685,722,
%U 761,800,841,882,925,968,1013,1058,1105,1152,1201,1250,1301,1352,1405,1458
%N Independence numbers for KT_2 knight on triangular board.
%H Colin Barker, <a href="/A087327/b087327.txt">Table of n, a(n) for n = 1..1000</a>
%H J.-P. Bode and H. Harborth, <a href="https://doi.org/10.1016/S0012-365X(03)00181-X">Independence for knights on hexagon and triangle boards</a>, Discrete Math., 272 (2003), 27-35.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = ceiling(n^2/2) except for n=3.
%F From _Colin Barker_, Feb 02 2016: (Start)
%F a(n) = (2*n^2-(-1)^n+1)/4 for n>3.
%F a(n) = n^2/2 for even n>3; a(n) = (n^2+1)/2 for odd n>3.
%F a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3.
%F G.f.: x*(1+2*x^2-2*x^3+2*x^5-x^6) / ((1-x)^3*(1+x)). (End)
%t LinearRecurrence[{2,0,-2,1},{1,2,6,8,13,18,25},60] (* _Harvey P. Dale_, Mar 14 2018 *)
%o (PARI) Vec(x*(1+2*x^2-2*x^3+2*x^5-x^6)/((1-x)^3*(1+x)) + O(x^100)) \\ _Colin Barker_, Feb 02 2016
%Y Cf. A000982, A030978, A087328, A087329.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Oct 21 2003
%E More terms from _David Wasserman_, May 06 2005
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