OFFSET
0,3
COMMENTS
Partial sums of A036405.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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,-3,1,0,0,0,1,-3,3,-1).
FORMULA
a(n) = round((2*n+1)*(n^2 + n + 12)/42).
a(n) = floor((n+1)*(2*n^2 + n + 24)/42).
a(n) = ceiling((2*n^3 + 3*n^2 + 25*n)/42).
a(n) = a(n-7) + (n+1)*(n-7) + 24, n > 6.
From R. J. Mathar, Dec 06 2010: (Start)
G.f.: x*(1+x)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1) / ( (x^6 + x^5 + 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-7) - 3*a(n-8) + 3*a(n-9) - a(n-10). (End)
EXAMPLE
a(7) = 0 + 1 + 1 + 2 + 3 + 4 + 6 + 7 = 24.
MAPLE
seq(round((2*n+1)*(n^2+n+12)/42), n=0..50)
MATHEMATICA
Ceiling[Range[0, 50]^2/7]//Accumulate (* Harvey P. Dale, Apr 12 2018 *)
PROG
(Magma) [&+[Ceiling(k^2/7): k in [0..n]]: n in [0..50]]; // Bruno Berselli, Apr 26 2011
(PARI) a(n)=(n+1)*(2*n^2+n+24)\42 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 05 2010
STATUS
approved