OFFSET
0,3
COMMENTS
Partial sums of A036409.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..870
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
FORMULA
a(n) = round((2*n+1)*(n^2 + n + 18)/66).
a(n) = floor((n+1)*(2*n^2 + n + 36)/66).
a(n) = ceiling((2*n^3 + 3*n^2 + 37*n)/66).
a(n) = a(n-11) + (n+1)*(n-11) + 52, n > 10.
G.f.: x*(1+x)*(x^2 - x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 - x^2 + 1) / ( (x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4 ). - R. J. Mathar, Dec 06 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14). - R. J. Mathar, Dec 06 2010
EXAMPLE
a(11) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 11 = 52.
MAPLE
seq(round((2*n+1)*(n^2+n+18)/66), n=0..50)
PROG
(Magma) [Floor((n+1)*(2*n^2+n+36)/66): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Dec 05 2010
STATUS
approved