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.

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

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