[seqfan] x(i-1) = ( x(i+1) - x(i)) mod M, period-N solutions?
Ron Hardin
rhhardin at att.net
Sat Sep 4 14:41:13 CEST 2010
T(N,M) is the number of nonzero solutions of x(i-1) = (x(i+1) - x(i)) mod M,
with period N
for N=12 M=10 there are 19 (including shifted multiplicities)
1 0 5 5 0 5 5 0 5 5 0 5 5
2 5 0 5 5 0 5 5 0 5 5 0 5
3 5 5 0 5 5 0 5 5 0 5 5 0
4 1 3 4 7 1 8 9 7 6 3 9 2
5 1 8 9 7 6 3 9 2 1 3 4 7
6 6 3 9 2 1 3 4 7 1 8 9 7
7 6 8 4 2 6 8 4 2 6 8 4 2
8 2 1 3 4 7 1 8 9 7 6 3 9
9 2 6 8 4 2 6 8 4 2 6 8 4
10 7 1 8 9 7 6 3 9 2 1 3 4
11 7 6 3 9 2 1 3 4 7 1 8 9
12 4 2 6 8 4 2 6 8 4 2 6 8
13 4 7 1 8 9 7 6 3 9 2 1 3
14 9 2 1 3 4 7 1 8 9 7 6 3
15 9 7 6 3 9 2 1 3 4 7 1 8
16 3 4 7 1 8 9 7 6 3 9 2 1
17 3 9 2 1 3 4 7 1 8 9 7 6
18 8 4 2 6 8 4 2 6 8 4 2 6
19 8 9 7 6 3 9 2 1 3 4 7 1
T(N,M) starts (rows N=1.. cols M=1..)
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0
0 0 0 0 4 0 0 0 0 4 0 0 0 0 4 0 0 0 0
0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0
0 3 0 15 0 3 0 15 0 3 0 15 0 3 0 15 0 3 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 8 0 4 8 0 0 8 4 0 8 0 0 44 0 0 8 0
0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3 18
0 0 0 0 0 0 0 0 0 0 120 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 3 0 15 4 3 0 63 0 19 0 15 0 3 4 63 0 3 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 3 0 3 0 3 0 3 0 3 10 3 0 3 0 3 0 3 0
0 0 8 0 4 8 48 0 8 4 0 8 0 48 44 0 0 8 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 3 0 15 0 3 0 15 0 3 0 15 0 3 0 15 0 3 360
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 24 0 0 0 0 24 120 0 0 0 24 0 0 0 0
full current table occasionally updated at
http://rhhardin.home.mindspring.com/current5.txt
Ideas, formulas, is it already in OEIS in some form...?
rhhardin at mindspring.com
rhhardin at att.net (either)
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