A175829 Partial sums of ceiling(n^2/11).
0, 1, 2, 3, 5, 8, 12, 17, 23, 31, 41, 52, 66, 82, 100, 121, 145, 172, 202, 235, 272, 313, 357, 406, 459, 516, 578, 645, 717, 794, 876, 964, 1058, 1157, 1263, 1375, 1493, 1618, 1750, 1889, 2035, 2188, 2349, 2518, 2694, 2879, 3072, 3273, 3483, 3702, 3930
Offset: 0
Examples
a(11) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 11 = 52.
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.
Programs
-
Magma
[Floor((n+1)*(2*n^2+n+36)/66): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
-
Maple
seq(round((2*n+1)*(n^2+n+18)/66),n=0..50)
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
Comments