OFFSET
0,2
COMMENTS
In the Julian calendar, a year is a leap year if and only if it is a multiple of 4 and all century years are leap years.
Assuming this fact, this sequence is periodic with a period of 28.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Time And Date, Repeating Calendar
Time And Date, Julian Calendar
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
FORMULA
From Colin Barker, Oct 17 2019: (Start)
G.f.: x*(1 - x + x^2)*(5 + 6*x + 6*x^2 + 6*x^3 + 5*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.
(End)
PROG
(PARI) for(i=0, 420, for(y=0, 420, if(((5*(y\4)+(y%4))%7)==((5*((y+i)\4)+((y+i)%4))%7), print1(i", "); break)))
(PARI) concat(0, Vec(x*(1 - x + x^2)*(5 + 6*x + 6*x^2 + 6*x^3 + 5*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^40))) \\ Colin Barker, Oct 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); [0] cat Coefficients(R!( x*(1-x+x^2)*(5+6*x+6*x^2+6*x^3+5*x^4)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)) )); // Marius A. Burtea, Oct 17 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Aswini Vaidyanathan, Nov 02 2013
STATUS
approved