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 A175724 Partial sums of floor(n^2/12). 1
 0, 0, 0, 0, 1, 3, 6, 10, 15, 21, 29, 39, 51, 65, 81, 99, 120, 144, 171, 201, 234, 270, 310, 354, 402, 454, 510, 570, 635, 705, 780, 860, 945, 1035, 1131, 1233, 1341, 1455, 1575, 1701, 1834, 1974, 2121, 2275, 2436, 2604, 2780, 2964, 3156, 3356 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Partial sums of A008724. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,1,-3,3,-1). 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^3 + 3*n^2 - 18*n)/72). a(n) = a(n-6) + (n-2)*(n-3)/2, n>5. a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-6) -3*a(n-7) +3*a(n-8) -a(n-9), n>8. G.f.: x^4/((x+1)*(x^2+x+1)*(x^2-x+1)*(x-1)^4). MAPLE A175724 := proc(n) add( floor(i^2/12) , i=0..n) ; end proc: MATHEMATICA Accumulate[Floor[Range[0, 49]^2/12]] PROG (MAGMA) [ &+[ Floor(j^2/12): j in [0..n] ]: n in [0..60] ]; (PARI) vector(61, n, round((2*(n-1)^3 +3*(n-1)^2 -18*(n-1))/72) ) \\ G. C. Greubel, Dec 05 2019 (Sage) [round((2*n^3 +3*n^2 -18*n)/72) for n in (0..60)] # G. C. Greubel, Dec 05 2019 CROSSREFS Cf. A008724. Sequence in context: A062099 A115650 A025745 * A335184 A101551 A227430 Adjacent sequences:  A175721 A175722 A175723 * A175725 A175726 A175727 KEYWORD nonn,easy AUTHOR Mircea Merca, Aug 18 2010 STATUS approved

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Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)