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A184551 Super-birthdays (falling on the same weekday), version 3 (birth within 2 and 3 years after a February 29). 2
0, 11, 17, 22, 28, 39, 45, 50, 56, 67, 73, 78, 84, 95, 101, 106, 112, 123, 129, 134, 140, 151, 157, 162, 168, 179, 185, 190, 196, 207, 213, 218, 224, 235, 241, 246, 252, 263, 269, 274, 280, 291, 297 (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.

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.: x*(11 + 6*x + 5*x^2 + 6*x^3)/((1 - x)*(1 - x^4)). [corrected by Georg Fischer, May 10 2019]

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 2 and 3 years after a Feb. 29:

1+2+1+1+1+2+1+1 +1+2+1 = 14, after 11 years,

1+1+2+1+1+1 = 7, 6 years later, age of  17,

2+1+1+1+2 = 7, 5 years later: age of 22,

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

and then the same cycles repeat.

MATHEMATICA

CoefficientList[Series[x*(11+6*x+5*x^2+6*x^3)/((1-x)*(1-x^4)), {x, 0, 50}], x] (* G. C. Greubel, Feb 22 2017 *)

PROG

(PARI) a(n)=[0, 11, 17, 22][n%4+1]+n\4*28

(PARI) my(x='x+O('x^50)); concat([0], Vec(x*(11+6*x+5*x^2+6*x^3)/((1-x)*(1-x^4)))) \\ G. C. Greubel, May 10 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x*(11+6*x+5*x^2+6*x^3)/((1-x)*(1-x^4)) )); // G. C. Greubel, May 10 2019

(Sage) (x*(11+6*x+5*x^2+6*x^3)/((1-x)*(1-x^4))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, May 10 2019

CROSSREFS

Cf. A184549, A184550, A184552.

Sequence in context: A325902 A050715 A006618 * A190039 A066074 A106563

Adjacent sequences:  A184548 A184549 A184550 * A184552 A184553 A184554

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)