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A140044
Sequence generated from the 5/5Z addition table considered as a matrix.
2
1, 20, 175, 2025, 19500, 200625, 1990625, 20012500, 199828125, 2000234375, 19996875000, 200004296875, 1999943359375, 20000078125000, 199998974609375, 2000001416015625, 19999981445312500, 200000025634765625, 1999999664306640625, 20000000463867187500
OFFSET
1,2
COMMENTS
Analogous sequence for Z/4Z = A095897; and for Z/3Z = A007070.
a(n)/a(n-1) tends to 10.
FORMULA
Consider the 5/5Z addition table considered as matrix X = [0,1,2,3,4; 1,2,3,4,0; 2,3,4,0,1; 3,4,0,1,2; 4,0,1,2,3]. Then a(n) = term (1,2) of X^n.
G.f.: -x*(25*x^3-50*x^2+10*x+1) / ((10*x-1)*(125*x^4-25*x^2+1)). - Colin Barker, May 25 2013
EXAMPLE
a(5) = 19500 since term (1,2) of X^5 = 19500.
MAPLE
a:= n-> (Matrix(5, (i, j)-> irem(i+j-2, 5))^n)[1, 2]:
seq(a(n), n=1..25); # Alois P. Heinz, May 25 2013
CROSSREFS
Sequence in context: A047819 A163689 A342387 * A027332 A159538 A091983
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Two terms corrected and more terms added by Colin Barker, May 25 2013
STATUS
approved