A036406 a(n) = ceiling(n^2/8).

0, 1, 1, 2, 2, 4, 5, 7, 8, 11, 13, 16, 18, 22, 25, 29, 32, 37, 41, 46, 50, 56, 61, 67, 72, 79, 85, 92, 98, 106, 113, 121, 128, 137, 145, 154, 162, 172, 181, 191, 200, 211, 221, 232, 242, 254, 265, 277, 288, 301, 313, 326, 338, 352, 365, 379, 392

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1)

Programs

Magma

[Ceiling(n^2/8):n in [0..60]]; // Vincenzo Librandi, Oct 21 2011

Maple

A036406:=n->ceil(n^2/8); seq(A036406(n), n=0..60); # Wesley Ivan Hurt, Feb 14 2014

Mathematica

Ceiling[Range[0,60]^2/8] (* or *) LinearRecurrence[{2,-1,0,1,-2,1},{0,1,1,2,2,4},60] (* Harvey P. Dale, Jun 21 2011 *)

PARI

a(n)=ceil(n^2/8) \\ Charles R Greathouse IV, Feb 14 2014

Formula

a(n) = (1/16)*(2n^2 + 9 - 5(-1)^n - 2(-1)^floor(n/2) + 2(-1)^floor((n-1)/2)). - Ralf Stephan, Jun 10 2005

G.f.: -x*(1-x-x^3+x^2+x^4) / ( (1+x)*(1+x^2)*(x-1)^3 ). - R. J. Mathar, Jan 22 2011

a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6); a(0)=0, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=4. - Harvey P. Dale, Jun 21 2011