A181120 Partial sums of round(n^2/12) (A069905).
0, 0, 0, 1, 2, 4, 7, 11, 16, 23, 31, 41, 53, 67, 83, 102, 123, 147, 174, 204, 237, 274, 314, 358, 406, 458, 514, 575, 640, 710, 785, 865, 950, 1041, 1137, 1239, 1347, 1461, 1581, 1708, 1841, 1981, 2128, 2282, 2443, 2612, 2788, 2972, 3164, 3364, 3572
Offset: 0
Examples
a(5) = 4 = 0 + 0 + 0 + 1 + 1 + 2.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..870
- D. Barrera, M. J. Ibáñez, and S. Remogna, On the construction of trivariate near-best quasi-interpolants based on C^2 quartic splines on type-6 tetrahedral partitions, Journal of Computational and Applied, 2016, Volume 311, February 2017, Pages 252-261.
- J. Brandts and A. Cihangir, Counting triangles that share their vertices with the unit n-cube, in Conference Applications of Mathematics 2013 in honor of the 70th birthday of Karel Segeth. Jan Brandts, Sergey Korotov, et al., eds., Institute of Mathematics AS CR, Prague 2013.
- Jan Brandts and Apo Cihangir, Enumeration and investigation of acute 0/1-simplices modulo the action of the hyperoctahedral group, arXiv preprint arXiv:1512.03044 [math.CO], 2015.
- 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 (2,0,-1,-1,0,2,-1).
Crossrefs
Partial sums of A069905.
Programs
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Maple
a:= n-> round(1/(72)*(2*n^(3)+3*n^(2)-6*n)): seq(a(n), n=0..50);
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PARI
a(n)=round(n*(2*n^2+3*n-6)/72) \\ Charles R Greathouse IV, May 23 2013
Formula
a(n) = round((2*n^3 + 3*n^2 - 6*n)/72).
a(n) = round((4*n^3 + 6*n^2 - 12*n - 7)/144).
a(n) = floor((2*n^3 + 3*n^2 - 6*n + 9)/72).
a(n) = ceiling((2*n^3 + 3*n^2 - 6*n + 9 - 16)/72).
a(n) = a(n-6) + (n^2 - 5*n + 8)/2, n > 5.
From R. J. Mathar, Oct 06 2010: (Start)
a(n) = (-1)^n/16 + n^3/36 - n^2/24 - n/12 + 7/144 - A049347(n)/9.
G.f.: x^4 / ( (1+x)*(1+x+x^2)*(x-1)^4 ). (End)
a(n) = A000601(n-3). - R. J. Mathar, Oct 11 2017
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