A081276 Floor(n^3/8).

0, 0, 1, 3, 8, 15, 27, 42, 64, 91, 125, 166, 216, 274, 343, 421, 512, 614, 729, 857, 1000, 1157, 1331, 1520, 1728, 1953, 2197, 2460, 2744, 3048, 3375, 3723, 4096, 4492, 4913, 5359, 5832, 6331, 6859, 7414, 8000, 8615, 9261, 9938, 10648, 11390, 12167, 12977

Offset: 0

Author

Paul Barry, Mar 15 2003

Keywords

• easy
• nonn

Comments

a(2n) = n^3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

Crossrefs

Cf. A002620, A011863, A038503.

Programs

Magma

[Floor(n^3/8): n in [0..50]]; // Vincenzo Librandi, Aug 07 2013

Mathematica

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 *)

Formula

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

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

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