A184550 Super-birthdays (falling on the same weekday), version 2 (birth within 1 and 2 years after a February 29).

0, 6, 11, 17, 28, 34, 39, 45, 56, 62, 67, 73, 84, 90, 95, 101, 112, 118, 123, 129, 140, 146, 151, 157, 168, 174, 179, 185, 196, 202, 207, 213, 224, 230, 235, 241, 252, 258, 263, 269, 280, 286, 291, 297

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.: (6 + 5*x + 6*x^2 + 11*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.
If you are born between 1 and 2 years after a Feb. 29:
1+1+2+1+1+1 = 7 after 6 years,
2+1+1+1+2 = 7, 5 years later: age of 11,
1+1+1 +2+1+1 = 7, 6 years later, i.e. age of 17,
1+2+1+1+1+2+1+1 +1+2+1 = 14, 11 years later: age of 28,
and then the same cycles repeat.

Mathematica

Join[{0}, CoefficientList[Series[(6 + 5*x + 6*x^2 + 11*x^3)/((-1 + x)^2*(1 + x + x^2 + x^3)), {x, 0, 50}], x]] (* G. C. Greubel, Feb 22 2017 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 6, 11, 17, 28}, 50] (* Harvey P. Dale, Nov 21 2019 *)

Prog

(PARI) a(n)=[0, 6, 11, 17][n%4+1]+n\4*28

Crossrefs

Cf. A184549-A184552.

Sequence in context: A315554 A126620 A271987 * A109330 A253425 A099225

Adjacent sequences: A184547 A184548 A184549 * A184551 A184552 A184553

Keyword

nonn

Author

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

Status

approved