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A130520
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a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266).
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19
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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
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OFFSET
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0,7
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COMMENTS
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Complementary with A130483 regarding triangular numbers, in that A130483(n)+5*a(n)=n(n+1)/2=A000217(n).
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LINKS
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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).
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FORMULA
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a(n) = 1/2*floor(n/5)*(2n-3-5*floor(n/5)).
a(n) = A002266(n)*(2n-3-5*A002266(n))/2.
a(n) = 1/2*A002266(n)*(n-3+A010874(n)).
G.f.: x^5/((1-x^5)(1-x)^2) = -x^5 / ( (x^4+x^3+x^2+x+1)*(x-1)^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
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MATHEMATICA
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Accumulate[Floor[Range[0, 70]/5]] (* Harvey P. Dale, May 25 2016 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Hieronymus Fischer, Jun 01 2007
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STATUS
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approved
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