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 A269640 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1. 11
 2, 3, 4, 4, 9, 6, 5, 16, 24, 9, 6, 25, 60, 63, 12, 7, 36, 120, 221, 159, 16, 8, 49, 210, 567, 796, 396, 20, 9, 64, 336, 1209, 2637, 2828, 969, 25, 10, 81, 504, 2279, 6876, 12125, 9928, 2349, 30, 11, 100, 720, 3933, 15307, 38738, 55225, 34537, 5640, 36, 12, 121, 990 (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 ..6....24.....60.....120......210.......336.......504........720........990 ..9....63....221.....567.....1209......2279......3933.......6351.......9737 .12...159....796....2637.....6876.....15307.....30444......55641......95212 .16...396...2828...12125....38738....101999....234080.....484673.....926390 .20...969...9928...55225...216528....675151...1789528....4200933....8974480 .25..2349..34537..249600..1202353...4443665..13613507...36254755...86609789 .30..5640.119236.1120868..6639294..29104549.103118640..311698647..833022466 .36.13455.409098.5006144.36486190.189818232.778158768.2670823421.7987993868 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) -2*a(n-3) +a(n-4) k=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) k=3: a(n) = 9*a(n-1) -21*a(n-2) -19*a(n-3) +93*a(n-4) +27*a(n-5) -133*a(n-6) -87*a(n-7) k=4: [order 7] k=5: [order 13] k=6: [order 14] k=7: [order 16] 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 + 2*n n=4: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1 n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 5*n + 1 n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 12*n^2 + 9*n - 7 for n>2 n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2 EXAMPLE Some solutions for n=6 k=4 ..4. .2. .3. .4. .3. .0. .2. .4. .0. .3. .1. .0. .4. .1. .0. .3 ..0. .3. .1. .2. .1. .0. .1. .3. .0. .4. .2. .2. .1. .3. .3. .2 ..3. .1. .2. .4. .4. .3. .4. .0. .1. .3. .0. .1. .0. .2. .0. .4 ..2. .4. .0. .3. .2. .1. .1. .2. .2. .0. .1. .0. .3. .0. .3. .0 ..1. .1. .2. .3. .2. .2. .3. .0. .4. .3. .0. .3. .2. .4. .1. .1 ..0. .4. .3. .0. .4. .1. .3. .2. .2. .0. .2. .0. .4. .1. .2. .1 CROSSREFS Column 1 is A002620(n+2). Column 2 is A268938. Row 1 is A000027(n+1). Row 2 is A000290(n+1). Row 3 is A007531(n+2). Sequence in context: A056877 A267232 A269606 * A269409 A268944 A269537 Adjacent sequences: A269637 A269638 A269639 * A269641 A269642 A269643 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 02 2016 STATUS approved

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