A131479 a(n) = floor(n^4/4).
0, 0, 4, 20, 64, 156, 324, 600, 1024, 1640, 2500, 3660, 5184, 7140, 9604, 12656, 16384, 20880, 26244, 32580, 40000, 48620, 58564, 69960, 82944, 97656, 114244, 132860, 153664, 176820, 202500, 230880, 262144, 296480, 334084, 375156
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).
Programs
-
Magma
[Floor(n^4/4): n in [0..60]]; // Vincenzo Librandi, Jun 16 2011
-
Maple
seq(op([4*k^4, 2*(k^3*(k+1)+k*(k+1)^3)]),k=0..100); # Robert Israel, Jun 01 2015
-
Mathematica
Table[Floor[n^4/4], {n, 0, 20}] (* Enrique Pérez Herrero, May 31 2015 *) -
PARI
vector(50, n, n--; n^4\4) \\ Michel Marcus, Jun 02 2015
-
Python
def A131479(n): return n**4>>2 # Chai Wah Wu, Jan 31 2023
Formula
From R. J. Mathar, Dec 19 2008: (Start)
G.f.: 4*x^2*(1+x+x^2)/((1+x)*(1-x)^5).
a(n) = 4*A011863(n-1). (End)
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
a(2*k) = 4*k^4; a(2*k+1) = 2*(k^3*(k+1) + k*(k+1)^3). - Robert Israel, Jun 01 2015
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