A248944 T(n,k)=Number of length n arrays x(i), i=1..n with x(i) in i..i+k and no value appearing more than 1 time.
2, 3, 3, 4, 7, 4, 5, 13, 14, 5, 6, 21, 36, 26, 6, 7, 31, 76, 90, 46, 7, 8, 43, 140, 246, 212, 79, 8, 9, 57, 234, 566, 738, 478, 133, 9, 10, 73, 364, 1146, 2104, 2108, 1044, 221, 10, 11, 91, 536, 2106, 5150, 7364, 5794, 2227, 364, 11, 12, 111, 756, 3590, 11196, 21652, 24720
Offset: 1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..507
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)
k=3: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-4) +4*a(n-5) -a(n-8)
k=4: [order 16]
k=5: [order 32]
k=6: [order 63]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + n + 1
n=3: a(n) = n^3 + 3*n
n=4: a(n) = n^4 - 2*n^3 + 9*n^2 - 8*n + 6 for n>1
n=5: a(n) = n^5 - 5*n^4 + 25*n^3 - 55*n^2 + 80*n - 46 for n>1
n=6: a(n) = n^6 - 9*n^5 + 60*n^4 - 225*n^3 + 555*n^2 - 774*n + 484 for n>3
n=7: a(n) = n^7 - 14*n^6 + 126*n^5 - 700*n^4 + 2625*n^3 - 6342*n^2 + 9072*n - 5840 for n>4
Comments