[seqfan] Time-Indepenent Schrodinger Equation discrete version

Ron Hardin rhhardin at att.net
Fri Feb 8 23:53:45 CET 2013


/tmp/czd
T(n,k)=Number of -k..k arrays of length n whose elements are some constant times 
the end-around second differences

Table starts
..3..5...7...9..11..13..15..17..19..21..23..25..27.29.31
..5..9..13..17..21..25..29..33..37..41..45..49..53.57...
..9.23..43..69.101.139.183.233.289.351.419.493.573......
.13.33..61..97.141.193.253.321.397.481.573.673..........
..3..5...7...9..11..13..15..17..19..21..23..............
.17.45..85.137.201.277.365.465.577.701..................
..3..5...7...9..11..13..15..17..19......................
.13.33..61..97.141.193.253.321..........................
..9.23..43..69.101.139.183..............................
..5..9..13..17..21..25..................................
..3..5...7...9..11......................................
.25.69.133..............................................
..3..5..................................................
..5.....................................................

*Empirical*
Columns all have period 12 following a pattern 1 2 3 4 5 6 5 4 3 2 1 0 1 2 3 4 
...
Rows are polynomials in k
formula (bc):
define t(n,k) {
    if(n%12==0)return 10*k^2+14*k+1;
    if(n%12==1||n%12==5||n%12==7||n%12==11)return 2*k+1;
    if(n%12==2||n%12==10)return 4*k+1;
    if(n%12==3||n%12==9)return 3*k^2+5*k+1;
    if(n%12==4||n%12==8)return 4*k^2+8*k+1;
    if(n%12==6)return 6*k^2+10*k+1;
}

Some examples for n=4 k=4
..1....3....3....3....1....0...-4....2...-4....0...-1....1....2...-4....1...-1
..3....3...-1...-3...-4....2....4...-3...-3....4....1....1...-1....0...-1...-3..
.-1...-3...-3...-3...-1....0....4...-2....4....0....1....1...-2....4...-1....1..
.-3...-3....1....3....4...-2...-4....3....3...-4...-1....1....1....0....1....3



 rhhardin at mindspring.com
rhhardin at att.net (either)



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