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A269640
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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.
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11
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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