|
Empirical: T(n,k) is symmetric for n and k both greater than 1.
Empirical for column k:
k=1: a(n) = 18*a(n-3) -32*a(n-6) for n>8
k=2: a(n) = 118*a(n-3) -4264*a(n-6) +55168*a(n-9) -225280*a(n-12) +262144*a(n-15) for n>16
k=3: a(n) = 454*a(n-3) -60040*a(n-6) +2444800*a(n-9) -13041664*a(n-12) +16777216*a(n-15) for n>16
k=4: a(n) = 260*a(n-3) -1024*a(n-6) for n>7
k=5: a(n) = 1804*a(n-3) -939040*a(n-6) +145285120*a(n-9) -1639972864*a(n-12) +4294967296*a(n-15) for n>16
k=6: a(n) = 7180*a(n-3) -14766112*a(n-6) +8766324736*a(n-9) -103548977152*a(n-12) +274877906944*a(n-15) for n>16
k=7: a(n) = 4104*a(n-3) -32768*a(n-6) for n>7
Empirical for row n:
n=1: a(n) = 34*a(n-3) +2*a(n-5) -320*a(n-6) -36*a(n-8) +512*a(n-9) +64*a(n-11) for n>15
n=2: a(n) = 118*a(n-3) -4264*a(n-6) +55168*a(n-9) -225280*a(n-12) +262144*a(n-15) for n>16
n=3: a(n) = 454*a(n-3) -60040*a(n-6) +2444800*a(n-9) -13041664*a(n-12) +16777216*a(n-15)
n=4: a(n) = 260*a(n-3) -1024*a(n-6)
n=5: a(n) = 1804*a(n-3) -939040*a(n-6) +145285120*a(n-9) -1639972864*a(n-12) +4294967296*a(n-15)
n=6: a(n) = 7180*a(n-3) -14766112*a(n-6) +8766324736*a(n-9) -103548977152*a(n-12) +274877906944*a(n-15)
n=7: a(n) = 4104*a(n-3) -32768*a(n-6)
| 