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 A242239 T(n,k)=Number of length n+k+1 0..k arrays with every value 0..k appearing at least once in every consecutive k+2 elements, and new values 0..k introduced in order 6
 3, 6, 5, 10, 12, 8, 15, 22, 22, 13, 21, 35, 43, 40, 21, 28, 51, 71, 82, 74, 34, 36, 70, 106, 139, 157, 136, 55, 45, 92, 148, 211, 271, 304, 250, 89, 55, 117, 197, 298, 416, 531, 586, 460, 144, 66, 145, 253, 400, 592, 821, 1047, 1129, 846, 233, 78, 176, 316, 517, 799 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ...3....6...10...15....21....28....36....45....55....66....78....91...105 ...5...12...22...35....51....70....92...117...145...176...210...247...287 ...8...22...43...71...106...148...197...253...316...386...463...547...638 ..13...40...82..139...211...298...400...517...649...796...958..1135..1327 ..21...74..157..271...416...592...799..1037..1306..1606..1937..2299..2692 ..34..136..304..531...821..1174..1590..2069..2611..3216..3884..4615..5409 ..55..250..586.1047..1626..2332..3165..4125..5212..6426..7767..9235.10830 ..89..460.1129.2059..3231..4642..6308..8229.10405.12836.15522.18463.21659 .144..846.2176.4047..6411..9256.12587.16429.20782.25646.31021.36907.43304 .233.1556.4195.7955.12716.18442.25138.32821.41527.51256.62008.73783.86581 LINKS R. H. Hardin, Table of n, a(n) for n = 1..731 FORMULA Empirical for column k: k=1: a(n) = a(n-1) +a(n-2) k=2: a(n) = a(n-1) +a(n-2) +a(n-3) k=3: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) k=4: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) k=5: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) k=6: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) k=7: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) k=8: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) k=9: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) Empirical for row n: n=1: a(n) = (1/2)*n^2 + (3/2)*n + 1 n=2: a(n) = (3/2)*n^2 + (5/2)*n + 1 n=3: a(n) = (7/2)*n^2 + (7/2)*n + 1 n=4: a(n) = (15/2)*n^2 + (9/2)*n + 1 n=5: a(n) = (31/2)*n^2 + (11/2)*n + 1 for n>1 n=6: a(n) = (63/2)*n^2 + (13/2)*n + 1 for n>2 n=7: a(n) = (127/2)*n^2 + (15/2)*n + 1 for n>3 n=8: a(n) = (255/2)*n^2 + (17/2)*n + 1 for n>4 n=9: a(n) = (511/2)*n^2 + (19/2)*n + 1 for n>5 n=10: a(n) = (1023/2)*n^2 + (21/2)*n + 1 for n>6 n=11: a(n) = (2047/2)*n^2 + (23/2)*n + 1 for n>7 n=12: a(n) = (4095/2)*n^2 + (25/2)*n + 1 for n>8 n=13: a(n) = (8191/2)*n^2 + (27/2)*n + 1 for n>9 n=14: a(n) = (16383/2)*n^2 + (29/2)*n + 1 for n>10 n=15: a(n) = (32767/2)*n^2 + (31/2)*n + 1 for n>11 Empirical large-k generalization, for k>n-4: T(n,k) = ((2^n-1)/2)*k^2 + ((2*n+1)/2)*k + 1 Empirical recurrence generalization, for column k: a(n) = sum {i in 1..k+1} a(n-i) EXAMPLE Some solutions for n=5 k=4 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..1....1....1....1....1....1....1....1....1....1....1....1....1....0....1....1 ..2....2....0....2....2....1....0....0....2....0....2....2....0....1....2....0 ..1....3....2....3....3....2....2....2....3....2....3....3....2....2....3....2 ..3....4....3....4....4....3....3....3....0....3....0....0....3....3....4....3 ..4....0....4....1....0....4....4....4....4....4....4....4....4....4....1....4 ..0....2....2....0....1....0....2....0....2....1....2....1....0....2....0....1 ..2....1....1....0....2....1....1....1....1....0....1....2....1....0....2....0 ..2....3....0....2....3....0....0....1....0....0....3....4....2....1....3....4 ..1....0....0....3....0....2....2....2....3....2....2....3....3....1....0....2 CROSSREFS Column 1 is A000045(n+3) Column 2 is A196700(n+3) Row 1 is A000217(n+1) Row 2 is A000326(n+1) Row 3 is A069099(n+1) Row 4 is A220083 Sequence in context: A310130 A298818 A196068 * A123089 A246978 A127780 Adjacent sequences:  A242236 A242237 A242238 * A242240 A242241 A242242 KEYWORD nonn,tabl AUTHOR R. H. Hardin, May 08 2014 STATUS approved

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Last modified June 16 04:44 EDT 2021. Contains 345056 sequences. (Running on oeis4.)