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%I #30 Mar 03 2024 17:50:05
%S 0,5,11,22,28,33,39,50,56,61,67,78,84,89,95,106,112,117,123,134,140,
%T 145,151,162,168,173,179,190,196,201,207,218,224,229,235,246,252,257,
%U 263,274,280,285,291,302,308,313,319,330,336,341,347,358,364,369,375
%N Super-birthdays (falling on the same weekday), version 4 (birth in the year preceding a February 29).
%C See example and the link for more explanation and limits of validity.
%C The offset is motivated by the special status of the initial term a(0)=0.
%D Alexandre Moatti, Récréations mathéphysiques, Editions le Pommier. ISBN: 9782746504875.
%H G. C. Greubel, <a href="/A184552/b184552.txt">Table of n, a(n) for n = 0..1000</a>
%H Charles R Greathouse IV, <a href="http://list.seqfan.eu/oldermail/seqfan/2011-January/006812.html">Re: Super-birthdays</a>, seqfan list, Jan 2011.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).
%F From _Alexander R. Povolotsky_, Jan 18 2011: (Start)
%F G.f.: (5 + 6*x + 11*x^2 + 6*x^3)/((-1 + x)^2*(1 + x + x^2 + x^3)).
%F a(n) = +1*a(n-1) + 1*a(n-4) - 1*a(n-5). (End)
%e A standard year has 365 = 350+14+1 = 1 (mod 7) days,
%e and a leap year has 366 = 2 (mod 7) days.
%e A super-birthday occurs when this sums up to a multiple of 7. For a birth in the year preceding a Feb 29:
%e 2+1+1+1+2 = 7, after 5 years,
%e 1+1+1 +2+1+1 = 7, 6 years later, i.e. age of 11,
%e 1+2+1+1+1+2+1+1 +1+2+1 = 14, 11 years later: age of 22,
%e 1+1+2+1+1+1 = 7, 6 years later, age of 28,
%e and then the same cycles repeat.
%t LinearRecurrence[{1, 0, 0, 1, -1}, {0, 5, 11, 22, 28}, 50] (* _G. C. Greubel_, Feb 19 2017 *)
%o (PARI) a(n)=[0, 5, 11, 22][n%4+1]+n\4*28
%Y Cf. A184549-A184551.
%K nonn
%O 0,2
%A _Eric Angelini_ and _M. F. Hasler_, Jan 16 2011
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