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A133879
n modulo 9 repeated 9 times.
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3
OFFSET
0,10
COMMENTS
Periodic with length 9^2=81.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1).
FORMULA
a(n)=(1+floor(n/9)) mod 9.
a(n)=1+floor(n/9)-9*floor((n+9)/81).
a(n)=(((n+9) mod 81)-(n mod 9))/9.
a(n)=((n+9-(n mod 9))/9) mod 9.
G.f. g(x)=(1-x^9)(1+2x^9+3x^18+4x^27+5x^36+6x^45+7x^56+8x^63)/((1-x)(1-x^81)).
G.f. g(x)=(1-x^9)*sum{0<=k<8, (k+1)*x^(9*k)}/((1-x)(1-x^81)).
G.f. g(x)=(8x^81-9x^72+1)/((1-x)(1-x^9)(1-x^81)).
MATHEMATICA
Rest[Flatten[Table[Table[Table[n, {9}], {n, 0, 8}], {3}], 1]]//Flatten (* Harvey P. Dale, Apr 15 2018 *)
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, Oct 10 2007
STATUS
approved