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A279169 a(n) = floor( 4*n^2/5 ).

%I A279169 #23 Sep 26 2022 05:39:34
%S A279169 0,0,3,7,12,20,28,39,51,64,80,96,115,135,156,180,204,231,259,288,320,
%T A279169 352,387,423,460,500,540,583,627,672,720,768,819,871,924,980,1036,
%U A279169 1095,1155,1216,1280,1344,1411,1479,1548,1620,1692,1767,1843,1920,2000,2080,2163,2247
%N A279169 a(n) = floor( 4*n^2/5 ).
%H A279169 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A279169 O.g.f.: x^2*(3 + x + x^2 + 3*x^3)/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).
%F A279169 a(n) = a(-n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7).
%F A279169 a(5*m+r) = 4*m*(5*m + 2*r) + a(r), where m >= 0 and 0 <= r < 5. Example: for m=4 and r=3, a(5*4+3) = a(23) = 4*4*(5*4 + 2*3) + a(3) = 416 + 7 = 423.
%F A279169 a(n) = A118015(2*n) = A008728(4*n+2) = A131242(4*n+4) = A014601(floor(2*n^2/5)).
%F A279169 Sum_{n>=2} 1/a(n) = Pi^2/120 + sqrt(29 - 62/sqrt(5))*Pi/8 + 5/16. - _Amiram Eldar_, Sep 26 2022
%t A279169 Table[Floor[4 n^2/5], {n, 0, 60}]
%t A279169 LinearRecurrence[{2,-1,0,0,1,-2,1},{0,0,3,7,12,20,28},60] (* _Harvey P. Dale_, Nov 07 2020 *)
%o A279169 (PARI) vector(60, n, n--; floor(4*n^2/5))
%o A279169 (Python) [int(4*n**2/5) for n in range(60)]
%o A279169 (Sage) [floor(4*n^2/5) for n in range(60)]
%o A279169 (Magma) [4*n^2 div 5: n in [0..60]];
%Y A279169 Cf. A090223: floor(4*n/5).
%Y A279169 Subsequence of A008728, A014601, A118015, A131242.
%Y A279169 Cf. similar sequences with closed form floor(k*n^2/5): A118015 (k=1), A033437 (k=2), A184535 (k=3).
%K A279169 nonn,easy
%O A279169 0,3
%A A279169 _Bruno Berselli_, Dec 07 2016