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A184552 Super-birthdays (falling on the same weekday), version 4 (birth in the year preceding a February 29). 4
0, 5, 11, 22, 28, 33, 39, 50, 56, 61, 67, 78, 84, 89, 95, 106, 112, 117, 123, 134, 140, 145, 151, 162, 168, 173, 179, 190, 196, 201, 207, 218, 224, 229, 235, 246, 252, 257, 263, 274, 280, 285, 291, 302, 308, 313, 319, 330, 336, 341, 347, 358, 364, 369, 375 (list; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 0..1000

Charles R Greathouse IV, Re: Super-birthdays, seqfan list, Jan 2011.

FORMULA

From Alexander R. Povolotsky, Jan 18 2011: (Start)

G.f.: (5 + 6*x + 11*x^2 + 6*x^3)/((-1 + x)^2*(1 + x + x^2 + x^3)).

a(n) = +1*a(n-1) + 1*a(n-4) - 1*a(n-5). (End)

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. For a birth in the year preceding a Feb 29:

2+1+1+1+2 = 7, after 5 years,

1+1+1 +2+1+1 = 7, 6 years later, i.e. age of 11,

1+2+1+1+1+2+1+1 +1+2+1 = 14, 11 years later: age of 22,

1+1+2+1+1+1 = 7, 6 years later, age of  28,

and then the same cycles repeat.

MATHEMATICA

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 5, 11, 22, 28}, 50] (* G. C. Greubel, Feb 19 2017 *)

PROG

(PARI) a(n)=[0, 5, 11, 22][n%4+1]+n\4*28

CROSSREFS

Cf. A184549-A184551.

Sequence in context: A261982 A296033 A296968 * A069097 A222548 A024921

Adjacent sequences:  A184549 A184550 A184551 * A184553 A184554 A184555

KEYWORD

nonn

AUTHOR

Eric Angelini and M. F. Hasler, Jan 16 2011

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)