A184552 Super-birthdays (falling on the same weekday), version 4 (birth in the year preceding a February 29).

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

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.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1).

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