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A133877
n modulo 7 repeated 7 times.
3
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,8
COMMENTS
Periodic with length 7^2=49.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1).
FORMULA
a(n)=(1+floor(n/7)) mod 7.
a(n)=1+floor(n/7)-7*floor((n+7)/49).
a(n)=(((n+7) mod 49)-(n mod 7))/7.
a(n)=((n+7-(n mod 7))/7) mod 7.
a(n)=binomial(n+7,n) mod 7 =binomial(n+7,7) mod 7.
G.f. g(x)=(1-x^7)(1+2x^7+3x^14+4x^21+5x^28+6x^35)/((1-x)(1-x^49)).
G.f. g(x)=(6x^49-7x^42+1)/((1-x)(1-x^7)(1-x^49)).
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Oct 10 2007
STATUS
approved