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a(n) = ceiling(n^4/4).
2

%I #41 Feb 19 2023 17:27:58

%S 0,1,4,21,64,157,324,601,1024,1641,2500,3661,5184,7141,9604,12657,

%T 16384,20881,26244,32581,40000,48621,58564,69961,82944,97657,114244,

%U 132861,153664,176821,202500,230881,262144,296481,334084,375157,419904,468541,521284

%N a(n) = ceiling(n^4/4).

%H Vincenzo Librandi, <a href="/A131478/b131478.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).

%F From _R. J. Mathar_, Dec 19 2008: (Start)

%F G.f.: x*(1 + 10*x^2 + x^4)/((1 - x)^5*(1 + x)).

%F a(n) + a(n+1) = A058919(n+1). (End)

%F a(n) = floor(n^4/4 + 3/4). - _Bruno Berselli_, Dec 21 2017

%F E.g.f.: (x*(x^3 + 6*x^2 + 7*x + 1)*cosh(x) + (x^4 + 6*x^3 + 7*x^2 + x + 3)*sinh(x))/4. - _Stefano Spezia_, Feb 18 2023

%t Ceiling[Range[0,40]^4/4] (* _Harvey P. Dale_, May 17 2019 *)

%t CoefficientList[Series[(x(x^3 + 6x^2 + 7x + 1)Cosh[x]+ (x^4 + 6x^3 + 7x^2 + x + 3)Sinh[x])/4,{x,0,35}],x]Table[n!,{n,0,35}] (* _Stefano Spezia_, Feb 19 2023 *)

%o (Magma) [Ceiling(n^4/4) : n in [0..50]]; // _Vincenzo Librandi_, Oct 01 2011

%o (PARI) vector(50, n, n--;ceil(n^4/4)) \\ _Michel Marcus_, Jun 16 2015

%o (Python)

%o def A131478(n): return n**4+3>>2 # _Chai Wah Wu_, Jan 30 2023

%Y Cf. A000982, A004526, A007590, A008619, A036487, A058919.

%Y Cf. A131479.

%K nonn,easy

%O 0,3

%A _Mohammad K. Azarian_, Jul 27 2007