|
| |
|
|
A130520
|
|
a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266.)
|
|
20
|
|
|
|
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
From Amiram Eldar, Sep 17 2022: (Start)
Sum_{n>=5} 1/a(n) = 518/45 - 2*sqrt(2*(sqrt(5)+5))*Pi/3.
Sum_{n>=5} (-1)^(n+1)/a(n) = 8*sqrt(5)*arccoth(3/sqrt(5))/3 + 92*log(2)/15 - 418/45. (End)
|
|
|
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,changed
|
|
|
AUTHOR
|
Hieronymus Fischer, Jun 01 2007
|
|
|
STATUS
|
approved
|
| |
|
|
