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A096386 Number of numbers <= n which are divisible by 2 or 3. 0
0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 41, 42, 43, 43, 44, 44, 45, 46, 47, 47, 48, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
First differences are 6-periodic.
REFERENCES
S. Ramanujan, Question 723, Collected Papers of Srinivasa Ramanujan, p. 332, Ed. G. H. Hardy et al., AMS Chelsea 2000.
LINKS
Michael Penn, A great floor equation by Ramanujan, YouTube video, 2021.
S. Ramanujan, Question 723, J. Ind. Math. Soc.
FORMULA
a(n) = [n/2] + [(n+3)/6] = [n/3] + [(n+2)/6] + [(n+4)/6].
G.f.: x^2*(1+x+x^2+x^4)/((1-x)*(1-x^6)).
a(-n) = -a(n-1)-1.
a(n) = 4 + a(n-6).
MATHEMATICA
CoefficientList[Series[x^2 (1 + x + x^2 + x^4)/((1 - x) (1 - x^6)), {x, 0, 73}], x] (* Michael De Vlieger, Apr 13 2016 *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 0, 1, 2, 3, 3, 4}, 80] (* Harvey P. Dale, Jul 04 2016 *)
PROG
(PARI) a(n) = floor(n/2) + floor((n+3)/6)
(PARI) a(n)=n\2+(n+3)\6
CROSSREFS
Sequence in context: A057365 A014245 A350969 * A257063 A273663 A135671
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Aug 05 2004
EXTENSIONS
New name based on Mar 13 2007 comment of Vladeta Jovovic. - Charles R Greathouse IV, Jan 10 2022
STATUS
approved

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)