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Floor(n^3/8).
2

%I #15 Sep 08 2022 08:45:09

%S 0,0,1,3,8,15,27,42,64,91,125,166,216,274,343,421,512,614,729,857,

%T 1000,1157,1331,1520,1728,1953,2197,2460,2744,3048,3375,3723,4096,

%U 4492,4913,5359,5832,6331,6859,7414,8000,8615,9261,9938,10648,11390,12167,12977

%N Floor(n^3/8).

%C a(2n) = n^3.

%H Vincenzo Librandi, <a href="/A081276/b081276.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

%F a(n) = floor(n^3/8).

%F G.f.: x^2*(-x^3-2*x^5+3*x^4+1+4*x^6+2*x^2-2*x^7+x^8)/((-1+x)^4*(1+x)*(1+x^2)*(x^4+1)). - _R. J. Mathar_, Jun 26 2009

%F a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=8, a(5)=15, a(6)=27, a(7)=42, a(8)=64, a(9)=91, a(10)=125, a(n)=3*a(n-1)-3*a(n-2)+a(n-3)+a(n-8)- 3*a(n-9)+ 3*a(n-10)-a (n-11). - _Harvey P. Dale_, Jan 27 2012

%t Floor[Range[0,50]^3/8] (* or *) LinearRecurrence[ {3,-3,1,0,0,0,0,1,-3,3,-1},{0,0,1,3,8,15,27,42,64,91,125},50] (* _Harvey P. Dale_, Jan 27 2012 *)

%o (Magma) [Floor(n^3/8): n in [0..50]]; // _Vincenzo Librandi_, Aug 07 2013

%Y Cf. A002620, A011863, A038503.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Mar 15 2003