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 A269494 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one. 12
 2, 3, 4, 4, 9, 8, 5, 16, 27, 14, 6, 25, 64, 77, 24, 7, 36, 125, 250, 215, 40, 8, 49, 216, 617, 964, 591, 66, 9, 64, 343, 1286, 3021, 3680, 1609, 108, 10, 81, 512, 2389, 7616, 14695, 13946, 4353, 176, 11, 100, 729, 4082, 16579, 44904, 71115, 52562, 11731, 286, 12, 121 (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 ..14....77....250.....617.....1286......2389.......4082.......6545.......9982 ..24...215....964....3021.....7616.....16579......32460......58649......99496 ..40...591...3680...14695....44904....114695.....257536.....524655.....990440 ..66..1609..13946...71115...263794....791381....2039274....4686391....9847970 .108..4353..52562..342749..1545030...5448185...16120298...41805237...97817054 .176.11731.197288.1646513..9026500..37435583..127240496..372491293..970685708 .286.31543.738190.7888637.52624694.256804141.1003029086.3315522725.9624545062 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) -a(n-3) k=2: a(n) = 6*a(n-1) -9*a(n-2) -4*a(n-3) +10*a(n-4) +4*a(n-5) 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) = 12*a(n-1) -43*a(n-2) +24*a(n-3) +75*a(n-4) +20*a(n-5) -a(n-6) 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 + 6*n^2 + 2*n + 1 n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1 n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 + 5*n^2 + 6*n - 1 n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 + 7*n^3 + 17*n^2 - n - 1 EXAMPLE Some solutions for n=6 k=4 ..1. .0. .1. .0. .1. .4. .2. .2. .0. .0. .1. .2. .1. .0. .3. .2 ..1. .4. .0. .3. .2. .2. .4. .1. .2. .2. .1. .4. .0. .1. .2. .0 ..0. .4. .4. .2. .3. .1. .1. .4. .3. .2. .1. .0. .4. .3. .4. .0 ..1. .2. .1. .0. .2. .3. .4. .3. .1. .2. .1. .4. .1. .4. .4. .1 ..1. .0. .3. .3. .3. .4. .0. .1. .2. .4. .2. .3. .0. .2. .2. .2 ..4. .2. .2. .4. .2. .0. .1. .3. .3. .1. .3. .0. .2. .0. .1. .0 CROSSREFS Column 1 is A019274(n+2). Row 1 is A000027(n+1). Row 2 is A000290(n+1). Row 3 is A000578(n+1). Sequence in context: A244832 A250351 A269690 * A269776 A269619 A269435 Adjacent sequences: A269491 A269492 A269493 * A269495 A269496 A269497 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 28 2016 STATUS approved

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Last modified February 5 12:28 EST 2023. Contains 360084 sequences. (Running on oeis4.)