

A184549


Superbirthdays (falling on the same weekday), version 1 (birth within the year following a February 29).


3



0, 6, 17, 23, 28, 34, 45, 51, 56, 62, 73, 79, 84, 90, 101, 107, 112, 118, 129, 135, 140, 146, 157, 163, 168, 174, 185, 191, 196, 202, 213, 219, 224, 230, 241, 247, 252, 258, 269, 275, 280, 286, 297, 303, 308, 314
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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

Table of n, a(n) for n=0..45.
Charles R Greathouse IV, Re: Superbirthdays, seqfan list, Jan 2011.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,1).


FORMULA

a(n) = a(n1)+a(n4)a(n5). G.f.: x*(5*x^3+6*x^2+11*x+6) / ((x1)^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 superbirthday 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.


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)/((x1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Nov 04 2013


CROSSREFS

Cf. A184550A184552.
Sequence in context: A277684 A009171 A012417 * A166025 A171786 A017461
Adjacent sequences: A184546 A184547 A184548 * A184550 A184551 A184552


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



