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 A130520 a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266.) 19
 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 81, 87, 93, 99, 105, 112, 119, 126, 133, 140, 148, 156, 164, 172, 180, 189, 198, 207, 216, 225, 235, 245, 255, 265, 275, 286, 297, 308, 319, 330, 342, 354, 366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Complementary with A130483 regarding triangular numbers, in that A130483(n) + 5*a(n) = n*(n+1)/2 = A000217(n). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1). FORMULA a(n) = floor(n/5)*(2*n - 3 - 5*floor(n/5))/2. a(n) = A002266(n)*(2*n - 3 - 5*A002266(n))/2. a(n) = A002266(n)*(n -3 +A010874(n))/2. G.f.: x^5/((1-x^5)*(1-x)^2) =  x^5/( (1+x+x^2+x^3+x^4)*(1-x)^3 ). a(n) = floor((n-1)*(n-2)/10). - Mitch Harris, Sep 08 2008 a(n) = round(n*(n-3)/10) = ceiling((n+1)*(n-4)/10) = round((n^2 - 3*n - 1)/10). - Mircea Merca, Nov 28 2010 a(n) = A008732(n-5), n > 4. - R. J. Mathar, Nov 22 2008 a(n) = a(n-5) + n - 4, n > 4. - Mircea Merca, Nov 28 2010 a(5n) = A000566(n), a(5n+1) = A005476(n), a(5n+2) = A005475(n), a(5n+3) = A147875(n), a(5n+4) = A028895(n). - Philippe Deléham, Mar 26 2013 MAPLE seq(floor((n-1)*(n-2)/10), n=0..70); # G. C. Greubel, Aug 31 2019 MATHEMATICA Accumulate[Floor[Range[0, 70]/5]] (* Harvey P. Dale, May 25 2016 *) PROG (MAGMA) [Round(n*(n-3)/10): n in [0..70]]; // Vincenzo Librandi, Jun 25 2011 (PARI) a(n) = sum(k=0, n, k\5); \\ Michel Marcus, May 13 2016 (Sage) [floor((n-1)*(n-2)/10) for n in (0..70)] # G. C. Greubel, Aug 31 2019 (GAP) List([0..70], n-> Int((n-1)*(n-2)/10)); # G. C. Greubel, Aug 31 2019 CROSSREFS Cf. A002264, A002265, A004526, A010872, A010873, A010874, A130481, A130482. Sequence in context: A262249 A248421 A008732 * A005706 A173345 A226091 Adjacent sequences:  A130517 A130518 A130519 * A130521 A130522 A130523 KEYWORD nonn,easy AUTHOR Hieronymus Fischer, Jun 01 2007 STATUS approved

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)