OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
FORMULA
a(n+1) - a(n) = A047624(n+2).
a(n) = floor((n + 1/8)^2).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>5.
G.f.: x*(1+2*x+2*x^2+3*x^3)/((1+x)*(x^2+1)*(1-x)^3). - R. J. Mathar, Feb 27 2010
a(n) = (8*n^2+2*n-3+i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1). - Wesley Ivan Hurt, Jun 04 2016
MAPLE
MATHEMATICA
Table[n^2+Floor[n/4], {n, 0, 50}] (* or *) LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 1, 4, 9, 17, 26}, 50] (* Harvey P. Dale, Nov 25 2011 *)
PROG
(PARI) a(n)=n^2+n\4 \\ Charles R Greathouse IV, Oct 16 2015
(Magma) [Floor((n + 1/8)^2) : n in [0..80]]; // Wesley Ivan Hurt, Jun 04 2016
(Python)
def A173562(n): return n**2+(n>>2) # Chai Wah Wu, Feb 02 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Feb 21 2010
STATUS
approved