login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 17 09:29 EDT 2021. Contains 343064 sequences. (Running on oeis4.)