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A215414 Unix epoch timestamp for start of year, beginning with 1970.

%I A215414 #30 May 29 2025 21:54:10
%S A215414 0,31536000,63072000,94694400,126230400,157766400,189302400,220924800,
%T A215414 252460800,283996800,315532800,347155200,378691200,410227200,
%U A215414 441763200,473385600,504921600,536457600,567993600,599616000,631152000,662688000,694224000,725846400,757382400
%N A215414 Unix epoch timestamp for start of year, beginning with 1970.
%C A215414 This is based on a naive multiplication of A033172 with a fixed number of seconds per year, 24*3600 = 86400. It ignores that leap years are not regularly occurring after 4 years (but after 400 years, note the formula that relates a(n+4) to a(n) and also the simple Mma implementation), ignores leap seconds, and any other influences that align the slowing down of the Earth rotation in an astronomical fixed coordinate system measured relative to atomic clocks. In summary, the use of "year" in the definition is not commensurate with years in standard astronomical or earth observational terms. - _R. J. Mathar_, Aug 21 2012
%H A215414 G. C. Greubel, <a href="/A215414/b215414.txt">Table of n, a(n) for n = 1..1000</a>
%H A215414 Wikipedia, <a href="http://en.wikipedia.org/wiki/Unix_time">Unix time</a>
%H A215414 Wikipedia, <a href="http://en.wikipedia.org/wiki/Leap_seconds">Leap second</a>
%H A215414 Wikipedia, <a href="http://en.wikipedia.org/wiki/Revised_Julian_calendar">Revised Julian Calendar</a>
%H A215414 Wikipedia, <a href="http://en.wikipedia.org/wiki/IERS">International Earth Rotation and Reference Systems Service</a>
%F A215414 From _Alexander R. Povolotsky_, Aug 20 2012: (Start)
%F A215414 a(n) = 10800*(2922*n + (-1)^n + (1+i)*(-i)^n + (1-i)*i^n - 2923).
%F A215414 a(n+4) = a(n) + 126230400.
%F A215414 G.f.: 86400*(365*x +365*x^2 +366*x^3 +365*x^4)/((1-x)^2*(1+x+x^2+x^3)). (End)
%t A215414 lst = {}; t = 86400; Do[e = t*(365*(n - 1) + Ceiling[n/4]); If[! Mod[n, 4] == 0, e = e - t]; AppendTo[lst, e], {n, 25}]; lst (* _Arkadiusz Wesolowski_, Aug 20 2012 *)
%t A215414 CoefficientList[Series[86400*(365*x + 365*x^2 + 366*x^3 + 365*x^4)/((x - 1)^2*(1 +x +x^2 +x^3)), {x,0,50}], x] (* _G. C. Greubel_, Feb 26 2017 *)
%o A215414 (PARI) x='x+O('x^50); Vec(86400*(365*x +365*x^2 +366*x^3 +365*x^4)/((1-x)^2*(1+x+x^2+x^3))) \\ _G. C. Greubel_, Feb 26 2017
%Y A215414 Cf. A033172, A193910.
%K A215414 easy,nonn,less
%O A215414 1,2
%A A215414 _Kyle Stern_, Aug 09 2012
%E A215414 a(11)-a(25) from _Arkadiusz Wesolowski_, Aug 20 2012