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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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 02 2016
STATUS
approved

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)