cp's OEIS Frontend

A250361 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 3 times.

%I A250361 #6 Jul 23 2025 12:20:45
%S A250361 2,3,4,4,9,8,5,16,27,16,6,25,64,81,32,7,36,125,255,243,64,8,49,216,
%T A250361 623,1016,729,128,9,64,343,1293,3094,4048,2187,256,10,81,512,2397,
%U A250361 7712,15365,16128,6561,512,11,100,729,4091,16700,45866,76300,64257,19683,1024,12
%N A250361 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 3 times.
%C A250361 Table starts
%C A250361 ....2.....3.......4.......5........6.........7..........8..........9.........10
%C A250361 ....4.....9......16......25.......36........49.........64.........81........100
%C A250361 ....8....27......64.....125......216.......343........512........729.......1000
%C A250361 ...16....81.....255.....623.....1293......2397.......4091.......6555.......9993
%C A250361 ...32...243....1016....3094.....7712.....16700......32608......58826......99704
%C A250361 ...64...729....4048...15365....45866....115963.....259106.....526505.....992530
%C A250361 ..128..2187...16128...76300...272760....803382....2052904....4698744....9854280
%C A250361 ..256..6561...64257..378880..1621963...5565230...16234706...41828450...97581710
%C A250361 ..512.19683..256012.1881364..9644496..38548644..128373416..371780050..964209084
%C A250361 .1024.59049.1020000.9342081.57346376.266998350.1015004124.3304106808.9514922752
%H A250361 R. H. Hardin, <a href="/A250361/b250361.txt">Table of n, a(n) for n = 1..447</a>
%F A250361 Empirical for column k:
%F A250361 k=1: a(n) = 2*a(n-1)
%F A250361 k=2: a(n) = 3*a(n-1)
%F A250361 k=3: a(n) = 4*a(n-1) -a(n-4)
%F A250361 k=4: a(n) = 5*a(n-1) -2*a(n-4) -11*a(n-5) +a(n-8)
%F A250361 k=5: [order 13]
%F A250361 k=6: [order 25]
%F A250361 k=7: [order 56]
%F A250361 Empirical for row n:
%F A250361 n=1: a(n) = n + 1
%F A250361 n=2: a(n) = n^2 + 2*n + 1
%F A250361 n=3: a(n) = n^3 + 3*n^2 + 3*n + 1
%F A250361 n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 3*n + 3 for n>1
%F A250361 n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 5*n^2 + 17*n + 2 for n>2
%F A250361 n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 5*n^3 + 57*n^2 + 13*n + 1 for n>3
%F A250361 n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 147*n^3 + 49*n^2 + 7*n for n>4
%e A250361 Some solutions for n=6 k=4
%e A250361 ..3....2....0....0....2....1....2....1....2....2....3....0....3....3....0....2
%e A250361 ..2....3....1....4....4....4....3....3....1....3....2....3....1....3....4....4
%e A250361 ..4....5....5....6....6....6....3....4....2....4....3....4....3....3....2....3
%e A250361 ..3....3....4....3....5....6....7....4....5....3....6....7....4....5....6....7
%e A250361 ..7....8....7....6....6....6....5....7....5....4....5....5....5....6....5....8
%e A250361 ..5....7....9....9....9....9....8....5....9....5....9....7....7....6....9....5
%Y A250361 Column 1 is A000079
%Y A250361 Column 2 is A000244
%Y A250361 Column 3 is A206450
%Y A250361 Row 1 is A000027(n+1)
%Y A250361 Row 2 is A000290(n+1)
%Y A250361 Row 3 is A000578(n+1)
%Y A250361 Cf. A248944, A250351
%K A250361 nonn,tabl
%O A250361 1,1
%A A250361 _R. H. Hardin_, Nov 19 2014