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

0, 31536000, 63072000, 94694400, 126230400, 157766400, 189302400, 220924800, 252460800, 283996800, 315532800, 347155200, 378691200, 410227200, 441763200, 473385600, 504921600, 536457600, 567993600, 599616000, 631152000, 662688000, 694224000, 725846400, 757382400

Offset: 1

Author

Kyle Stern, Aug 09 2012

Keywords

• easy
• nonn
• less

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Wikipedia, Unix time
• Wikipedia, Leap second
• Wikipedia, Revised Julian Calendar
• Wikipedia, International Earth Rotation and Reference Systems Service

Crossrefs

Cf. A033172, A193910.

Programs

Mathematica

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 *)
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 *)

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

Formula

From Alexander R. Povolotsky, Aug 20 2012: (Start)

a(n) = 10800*(2922*n + (-1)^n + (1+i)*(-i)^n + (1-i)*i^n - 2923).

a(n+4) = a(n) + 126230400.

G.f.: 86400*(365*x +365*x^2 +366*x^3 +365*x^4)/((1-x)^2*(1+x+x^2+x^3)). (End)

Extensions

a(11)-a(25) from Arkadiusz Wesolowski, Aug 20 2012