OFFSET
0,2
COMMENTS
See example and the link for more explanation and limits of validity.
The offset is motivated by the special status of the initial term a(0)=0.
REFERENCES
Alexandre Moatti, Récréations mathéphysiques, Editions le Pommier. ISBN: 9782746504875.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
Charles R Greathouse IV, Re: Super-birthdays, seqfan list, Jan 2011.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(5*x^3+6*x^2+11*x+6) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Nov 04 2013
EXAMPLE
A standard year has 365 = 350+14+1 = 1 (mod 7) days,
and a leap year has 366 = 2 (mod 7) days.
A super-birthday occurs when this sums up to a multiple of 7.
If you are born in the year following a Feb 29:
1+1+1+2+1+1 = 7 after 6 years,
1+2+1+1+1+2+1+1 +1+2+1 = 14, 11 years later, i.e. age of 17,
1+1+2+1+1+1 = 7, 6 years later: age of 23,
2+1+1+1+2 = 7, 5 years later: age of 28,
and then the same cycles repeat.
MATHEMATICA
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 6, 17, 23, 28}, 100] (* Paolo Xausa, Mar 17 2024 *)
PROG
(PARI) a(n)=[0, 6, 17, 23][n%4+1]+n\4*28
(PARI) Vec(x*(5*x^3+6*x^2+11*x+6)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Nov 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric Angelini and M. F. Hasler, Jan 16 2011
STATUS
approved