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A215414
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Unix epoch timestamp for start of year, beginning with 1970.
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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