OFFSET
0,6
LINKS
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,1,-3,3,-1).
FORMULA
a(n) = Sum_{k=0..n} floor(k^2/10).
a(n) = a(n-10)+(n-5)^2+n-1 , n>9.
From R. J. Mathar, Nov 24 2010: (Start)
G.f.: x^4*(1+x^4) / ( (1+x)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^4 ).
a(n)= +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-10) -3*a(n-11) +3*a(n-12) -a(n-13). (End)
a(n) = floor((2*n^3+3*n^2-26*n+24)/60) + floor((n+1)/10) - floor((n+3)/10). - Hoang Xuan Thanh, Jun 02 2025
EXAMPLE
a(9) = 0+0+0+0+1+2+3+4+6+8 = 24.
MATHEMATICA
Accumulate[Floor[Range[0, 50]^2/10]] (* Harvey P. Dale, May 31 2012 *)
PROG
(PARI) a(n)=(2*n^3+3*n^2-26*n)\/60 - ((n+3)%10<2) \\ Charles R Greathouse IV, Jun 02 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Nov 24 2010
STATUS
approved