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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.

%I A248944 #6 Jul 23 2025 11:47:46
%S A248944 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,
%T A248944 79,8,9,57,234,566,738,478,133,9,10,73,364,1146,2104,2108,1044,221,10,
%U A248944 11,91,536,2106,5150,7364,5794,2227,364,11,12,111,756,3590,11196,21652,24720
%N 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.
%C A248944 Table starts
%C A248944 ..2...3....4......5......6.......7........8........9........10........11
%C A248944 ..3...7...13.....21.....31......43.......57.......73........91.......111
%C A248944 ..4..14...36.....76....140.....234......364......536.......756......1030
%C A248944 ..5..26...90....246....566....1146.....2106.....3590......5766......8826
%C A248944 ..6..46..212....738...2104....5150....11196....22162.....40688.....70254
%C A248944 ..7..79..478...2108...7364...21652....55532...127604....268108....523244
%C A248944 ..8.133.1044...5794..24720...86608...260720...693552...1666000...3675680
%C A248944 ..9.221.2227..15458..80196..334072..1173240..3598120...9856552..24553080
%C A248944 .10.364.4664..40296.253072.1249768..5112544.17990600..56010096.157175032
%C A248944 .11.596.9627.103129.780902.4557284.21670160.87396728.308055528.971055240
%H A248944 R. H. Hardin, <a href="/A248944/b248944.txt">Table of n, a(n) for n = 1..507</a>
%F A248944 Empirical for column k:
%F A248944 k=1: a(n) = 2*a(n-1) -a(n-2)
%F A248944 k=2: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)
%F A248944 k=3: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-4) +4*a(n-5) -a(n-8)
%F A248944 k=4: [order 16]
%F A248944 k=5: [order 32]
%F A248944 k=6: [order 63]
%F A248944 Empirical for row n:
%F A248944 n=1: a(n) = n + 1
%F A248944 n=2: a(n) = n^2 + n + 1
%F A248944 n=3: a(n) = n^3 + 3*n
%F A248944 n=4: a(n) = n^4 - 2*n^3 + 9*n^2 - 8*n + 6 for n>1
%F A248944 n=5: a(n) = n^5 - 5*n^4 + 25*n^3 - 55*n^2 + 80*n - 46 for n>1
%F A248944 n=6: a(n) = n^6 - 9*n^5 + 60*n^4 - 225*n^3 + 555*n^2 - 774*n + 484 for n>3
%F A248944 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
%Y A248944 Column 1 is A000027(n+1)
%Y A248944 Column 2 is A001924(n+1)
%Y A248944 Column 3 is A079922
%Y A248944 Column 4 is A079923
%Y A248944 Column 5 is A079924
%Y A248944 Column 6 is A079925
%Y A248944 Column 7 is A079926
%Y A248944 Row 1 is A000027(n+1)
%Y A248944 Row 2 is A002061(n+1)
%Y A248944 Row 3 is A061989(n+3)
%Y A248944 Row 4 is A079909
%Y A248944 Row 5 is A079910
%Y A248944 Row 6 is A079911
%Y A248944 Row 7 is A079912
%K A248944 nonn,tabl
%O A248944 1,1
%A A248944 _R. H. Hardin_, Oct 17 2014