A250351 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 2 times.
2, 3, 4, 4, 9, 8, 5, 16, 26, 16, 6, 25, 62, 75, 32, 7, 36, 122, 235, 216, 64, 8, 49, 212, 581, 888, 622, 128, 9, 64, 338, 1221, 2724, 3349, 1791, 256, 10, 81, 506, 2287, 6900, 12734, 12620, 5157, 512, 11, 100, 722, 3935, 15186, 38543, 59406, 47545, 14849, 1024, 12
Offset: 1
Examples
Some solutions for n=6 k=4 ..2....3....2....0....4....2....4....3....4....0....3....1....0....4....4....4 ..3....1....2....1....3....2....1....4....1....4....5....4....5....4....5....1 ..3....4....4....4....2....3....4....5....5....2....4....5....6....6....3....2 ..5....7....7....4....5....6....5....3....4....5....4....6....5....6....6....5 ..7....6....7....7....7....6....5....5....7....6....8....5....7....7....7....7 ..9....6....9....9....6....5....9....8....7....6....5....6....8....5....7....9
Links
- R. H. Hardin, Table of n, a(n) for n = 1..418
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-3)
k=3: a(n) = 4*a(n-1) -2*a(n-3) -5*a(n-4) +a(n-6) = A250346(n)
k=4: [order 12] = A250347(n)
k=5: [order 24] = A250348(n)
k=6: [order 48] = A250349(n).
k=7: [order 96] = A250350(n).
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 2*n + 2 = A250352(n).
n=4: a(n) = n^4 + 4*n^3 + 2*n^2 + 9*n + 1 for n>1 = A250353(n).
n=5: a(n) = n^5 + 5*n^4 + 25*n^2 + 5*n for n>2 = A250354(n).
n=6: a(n) = n^6 + 6*n^5 - 5*n^4 + 55*n^3 + 25*n^2 - 61*n + 98 for n>3 = A250355(n).
n=7: a(n) = n^7 + 7*n^6 - 14*n^5 + 105*n^4 + 105*n^3 - 532*n^2 + 1252*n - 744 for n>4 = A250356(n).
Comments