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

1,1

Comments

Table starts

..2...3....4......5......6.......7........8........9........10........11

..3...7...13.....21.....31......43.......57.......73........91.......111

..4..14...36.....76....140.....234......364......536.......756......1030

..5..26...90....246....566....1146.....2106.....3590......5766......8826

..6..46..212....738...2104....5150....11196....22162.....40688.....70254

..7..79..478...2108...7364...21652....55532...127604....268108....523244

..8.133.1044...5794..24720...86608...260720...693552...1666000...3675680

..9.221.2227..15458..80196..334072..1173240..3598120...9856552..24553080

.10.364.4664..40296.253072.1249768..5112544.17990600..56010096.157175032

.11.596.9627.103129.780902.4557284.21670160.87396728.308055528.971055240

Links

R. H. Hardin, Table of n, a(n) for n = 1..507

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

Crossrefs

Column 1 is A000027(n+1)

Column 2 is A001924(n+1)

Column 3 is A079922

Column 4 is A079923

Column 5 is A079924

Column 6 is A079925

Column 7 is A079926

Row 1 is A000027(n+1)

Row 2 is A002061(n+1)

Row 3 is A061989(n+3)

Row 4 is A079909

Row 5 is A079910

Row 6 is A079911

Row 7 is A079912

Sequence in context: A266362 A241956 A227125 * A267245 A266428 A180985

Adjacent sequences: A248941 A248942 A248943 * A248945 A248946 A248947

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 17 2014

Status

approved