A140044 Sequence generated from the 5/5Z addition table considered as a matrix.

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.

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (10,25,-250,-125,1250).

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

Cf. A007070, A095897.

Sequence in context: A047819 A163689 A342387 * A027332 A159538 A091983

Adjacent sequences: A140041 A140042 A140043 * A140045 A140046 A140047

Keyword

nonn,easy

Author

Gary W. Adamson and Roger L. Bagula, May 02 2008

Extensions

Two terms corrected and more terms added by Colin Barker, May 25 2013

Status

approved