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A130520 a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266). 19

%I

%S 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,

%T 65,70,75,81,87,93,99,105,112,119,126,133,140,148,156,164,172,180,189,

%U 198,207,216,225,235,245,255,265,275,286,297,308,319,330,342,354,366

%N a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266).

%C Complementary with A130483 regarding triangular numbers, in that A130483(n)+5*a(n)=n(n+1)/2=A000217(n).

%H Vincenzo Librandi, <a href="/A130520/b130520.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).

%F a(n) = 1/2*floor(n/5)*(2n-3-5*floor(n/5)).

%F a(n) = A002266(n)*(2n-3-5*A002266(n))/2.

%F a(n) = 1/2*A002266(n)*(n-3+A010874(n)).

%F G.f.: x^5/((1-x^5)(1-x)^2) = -x^5 / ( (x^4+x^3+x^2+x+1)*(x-1)^3 ).

%F a(n) = floor((n-1)(n-2)/10). [_Mitch Harris_, Sep 08 2008]

%F 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]

%F a(n) = A008732(n-5), n>4. [_R. J. Mathar_, Nov 22 2008]

%F a(n) = a(n-5)+n-4, n>4. [_Mircea Merca_, Nov 28 2010]

%F 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

%t Accumulate[Floor[Range[0,70]/5]] (* _Harvey P. Dale_, May 25 2016 *)

%o (MAGMA) [Round(n*(n-3)/10): n in [0..70]]; // _Vincenzo Librandi_, Jun 25 2011

%o (PARI) a(n) = sum(k=0, n, k\5); \\ _Michel Marcus_, May 13 2016

%Y Cf. A002264, A002265, A004526, A010872, A010873, A010874, A130481, A130482.

%K nonn,easy

%O 0,7

%A _Hieronymus Fischer_, Jun 01 2007

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)