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 A269583 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by more than one. 11
 2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 64, 79, 32, 7, 36, 125, 250, 229, 64, 8, 49, 216, 613, 964, 659, 128, 9, 64, 343, 1276, 2969, 3680, 1889, 256, 10, 81, 512, 2371, 7456, 14239, 13946, 5401, 512, 11, 100, 729, 4054, 16237, 43184, 67763, 52562, 15419, 1024, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....2.....3......4.......5........6.........7.........8..........9.........10 ....4.....9.....16......25.......36........49........64.........81........100 ....8....27.....64.....125......216.......343.......512........729.......1000 ...16....79....250.....613.....1276......2371......4054.......6505.......9928 ...32...229....964....2969.....7456.....16237.....31844......57649......97984 ...64...659...3680...14239....43184....110339....248464.....507935.....962144 ..128..1889..13946...67763...248324....745013...1927694....4453031....9406088 ..256..5401..52562..320495..1419502...5003189..14883506...38870827...91601150 ..512.15419.197288.1508267..8074172..33444515.114432704..338024963..889023812 .1024.43977.738190.7069055.45734140.222678103.876609410.2929722175.8602245520 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) +a(n-4) k=3: a(n) = 9*a(n-1) -24*a(n-2) +9*a(n-3) +26*a(n-4) +3*a(n-5) k=4: a(n) = 16*a(n-1) -93*a(n-2) +220*a(n-3) -112*a(n-4) -192*a(n-5) -2*a(n-6) +8*a(n-7) k=5: [order 7] k=6: [order 9] k=7: [order 9] Empirical for row n: n=1: a(n) = n + 1 n=2: a(n) = n^2 + 2*n + 1 n=3: a(n) = n^3 + 3*n^2 + 3*n + 1 n=4: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n + 1 n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 6*n + 1 n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 15*n^2 + 12*n - 1 n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 28*n^3 + 42*n^2 + 5*n - 1 EXAMPLE Some solutions for n=6 k=4 ..4. .1. .1. .4. .0. .0. .4. .3. .1. .4. .3. .0. .4. .3. .1. .0 ..4. .2. .0. .2. .0. .2. .3. .3. .2. .3. .1. .1. .2. .0. .3. .2 ..2. .3. .1. .4. .1. .1. .3. .1. .4. .4. .3. .1. .4. .0. .3. .0 ..3. .3. .2. .1. .3. .0. .4. .0. .0. .3. .0. .3. .0. .3. .4. .2 ..4. .2. .2. .4. .0. .0. .1. .1. .0. .0. .0. .1. .3. .0. .2. .4 ..1. .4. .3. .1. .0. .1. .2. .4. .0. .1. .3. .2. .1. .2. .3. .4 CROSSREFS Column 1 is A000079. Column 3 is A269489. Row 1 is A000027(n+1). Row 2 is A000290(n+1). Row 3 is A000578(n+1). Sequence in context: A223949 A224133 A228740 * A250361 A202784 A118263 Adjacent sequences: A269580 A269581 A269582 * A269584 A269585 A269586 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 01 2016 STATUS approved

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Last modified September 24 19:02 EDT 2023. Contains 365581 sequences. (Running on oeis4.)