%I
%S 3,17,43,81,131,193,267,353,451,561,683,817,963,1121,1291,1473,1667,
%T 1873,2091,2321,2563,2817,3083,3361,3651,3953,4267,4593,4931,5281,
%U 5643,6017,6403,6801,7211,7633,8067,8513,8971,9441,9923,10417,10923,11441
%N a(n) is the number of integer lattice points inside the right triangle with legs 3n and 4n (and hypotenuse 5n).
%C Row sums of triangle A193832.  _Omar E. Pol_, Aug 22 2011
%H Vincenzo Librandi, <a href="/A126587/b126587.txt">Table of n, a(n) for n = 1..10000</a>
%H Zak Seidov <a href="http://web.archive.org/web/20091026222954/http://geocities.com/zseidov/InsidePoints.html">Inside points</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,1).
%F a(n) = A186424(2*n1).
%F By Pick's theorem, a(n) = 6*n^2  4*n + 1.  Nick Hobson (nickh(AT)qbyte.org), Mar 13 2007
%F O.g.f.: x*(3+8*x+x^2)/(1x)^3 = 1  12/(1+x)^3  11/(1+x)  22/(1+x)^2.  _R. J. Mathar_, Dec 10 2007
%e At n=1, three lattice points (1,1), (1,2) and (2,1) are inside the triangle with vertices at the points (0,0), (3n,0) and (0,4n); hence a(1)=3.
%t nip[a_,b_]:=Sum[Floor[bb*i/a10^6],{i,a1}] Table[nip[3k,4k],{k,100}]
%t Table[6*n^24*n+1, {n,1,50}] (* _G. C. Greubel_, Mar 06 2018 *)
%o (MAGMA) [6*n^2  4*n + 1: n in [1..50] ]; // _Vincenzo Librandi_, May 23 2011
%o (PARI) a(n)=6*n^24*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 1,1
%A _Zak Seidov_, Jan 05 2007
