login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130520 a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266). 18
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) = 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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 28 11:45 EDT 2017. Contains 284186 sequences.