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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 3
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 17 2014
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)