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A131479 a(n) = floor(n^4/4).

%I A131479 #50 Feb 18 2023 19:02:30
%S A131479 0,0,4,20,64,156,324,600,1024,1640,2500,3660,5184,7140,9604,12656,
%T A131479 16384,20880,26244,32580,40000,48620,58564,69960,82944,97656,114244,
%U A131479 132860,153664,176820,202500,230880,262144,296480,334084,375156
%N A131479 a(n) = floor(n^4/4).
%H A131479 Vincenzo Librandi, <a href="/A131479/b131479.txt">Table of n, a(n) for n = 0..1000</a>
%H A131479 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F A131479 From _R. J. Mathar_, Dec 19 2008: (Start)
%F A131479 G.f.: 4*x^2*(1+x+x^2)/((1+x)*(1-x)^5).
%F A131479 a(n) = 4*A011863(n-1). (End)
%F A131479 a(n) = floor(n^2/2)*ceiling(n^2/2) = A007590(n) * A000982(n). - _Enrique Pérez Herrero_, May 31 2015
%F A131479 Sum_{n>=2} 1/a(n) = Sum_{n>=1} 1/(4n^4) + Sum_{n>=1} 1/(2n*(n+1)*(2n^2+2n+1)) = Zeta(4)/4 + (3-Pi*tanh(Pi/2))/2. - _Enrique Pérez Herrero_, May 31 2015
%F A131479 a(2*k) = 4*k^4; a(2*k+1) = 2*(k^3*(k+1) + k*(k+1)^3). - _Robert Israel_, Jun 01 2015
%F A131479 E.g.f.: (x*(x^3 + 6*x^2 + 7*x + 1)*cosh(x) + (x^4 + 6*x^3 + 7*x^2 + x - 1)*sinh(x))/4. - _Stefano Spezia_, Feb 18 2023
%p A131479 seq(op([4*k^4, 2*(k^3*(k+1)+k*(k+1)^3)]),k=0..100); # _Robert Israel_, Jun 01 2015
%t A131479 Table[Floor[n^4/4], {n, 0, 20}] (* _Enrique Pérez Herrero_, May 31 2015 *)
%o A131479 (Magma) [Floor(n^4/4): n in [0..60]]; // _Vincenzo Librandi_, Jun 16 2011
%o A131479 (PARI) vector(50, n, n--; n^4\4) \\ _Michel Marcus_, Jun 02 2015
%o A131479 (Python)
%o A131479 def A131479(n): return n**4>>2 # _Chai Wah Wu_, Jan 31 2023
%Y A131479 Cf. A000982, A004526, A007590, A008619, A011863, A036487.
%Y A131479 Cf. A131478.
%K A131479 nonn,easy
%O A131479 0,3
%A A131479 _Mohammad K. Azarian_, Jul 27 2007