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%I #31 Apr 24 2024 17:20:50
%S 0,4,17,37,66,102,147,199,260,328,405,489,582,682,791,907,1032,1164,
%T 1305,1453,1610,1774,1947,2127,2316,2512,2717,2929,3150,3378,3615,
%U 3859,4112,4372,4641,4917,5202,5494,5795,6103,6420,6744,7077,7417,7766,8122
%N a(n) = 4*n^2 + floor(n/2).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = floor((2*n + 1/8)^2).
%F a(n+1) - a(n) = A173512(n).
%F a(n) = A002943(n) - A007494(n) = A007742(n) - A110654(n).
%F a(2*n) = A157474(n) for n>0.
%F From - _R. J. Mathar_, Feb 21 2010: (Start)
%F a(n)= 2*a(n-1) -2*a(n-3) +a(n-4).
%F G.f.: -x*(4+9*x+3*x^2)/((1+x)*(x-1)^3). (End)
%F E.g.f.: (x*(8*x + 9)*cosh(x) + (8*x^2 + 9*x - 1)*sinh(x))/2. - _Stefano Spezia_, Apr 24 2024
%e a(6) = 147; 4(6)^2 + floor(6/3) = 144 + 3 = 147.
%p A173511:=n->4*n^2 + floor(n/2); seq(A173511(k), k=0..100); # _Wesley Ivan Hurt_, Nov 01 2013
%t Table[4n^2 + Floor[n/2], {n,0,100}] (* _Wesley Ivan Hurt_, Nov 01 2013 *)
%t LinearRecurrence[{2,0,-2,1},{0,4,17,37},50] (* _Harvey P. Dale_, Nov 23 2019 *)
%o (PARI) a(n) = 4*n^2 + n\2 \\ _Charles R Greathouse IV_, Jun 11 2015
%o (Python)
%o def A173511(n): return (n**2<<2)+(n>>1) # _Chai Wah Wu_, Jan 18 2023
%Y Cf. A002943, A007494, A007742, A110654, A157474, A173512.
%K nonn,easy
%O 0,2
%A _Reinhard Zumkeller_, Feb 20 2010
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