A184549 Super-birthdays (falling on the same weekday), version 1 (birth within the year following a February 29).

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

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

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(5*x^3+6*x^2+11*x+6) / ((x-1)^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 super-birthday 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.

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 6, 17, 23, 28}, 100] (* Paolo Xausa, Mar 17 2024 *)

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

Crossrefs

Cf. A184550, A184551, A184552.

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