A269494 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one.

2, 3, 4, 4, 9, 8, 5, 16, 27, 14, 6, 25, 64, 77, 24, 7, 36, 125, 250, 215, 40, 8, 49, 216, 617, 964, 591, 66, 9, 64, 343, 1286, 3021, 3680, 1609, 108, 10, 81, 512, 2389, 7616, 14695, 13946, 4353, 176, 11, 100, 729, 4082, 16579, 44904, 71115, 52562, 11731, 286, 12, 121

Offset

1,1

Comments

Table starts

...2.....3......4.......5........6.........7..........8..........9.........10

...4.....9.....16......25.......36........49.........64.........81........100

...8....27.....64.....125......216.......343........512........729.......1000

..14....77....250.....617.....1286......2389.......4082.......6545.......9982

..24...215....964....3021.....7616.....16579......32460......58649......99496

..40...591...3680...14695....44904....114695.....257536.....524655.....990440

..66..1609..13946...71115...263794....791381....2039274....4686391....9847970

.108..4353..52562..342749..1545030...5448185...16120298...41805237...97817054

.176.11731.197288.1646513..9026500..37435583..127240496..372491293..970685708

.286.31543.738190.7888637.52624694.256804141.1003029086.3315522725.9624545062

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) -a(n-3)

k=2: a(n) = 6*a(n-1) -9*a(n-2) -4*a(n-3) +10*a(n-4) +4*a(n-5)

k=3: a(n) = 9*a(n-1) -24*a(n-2) +9*a(n-3) +26*a(n-4) +3*a(n-5)

k=4: a(n) = 12*a(n-1) -43*a(n-2) +24*a(n-3) +75*a(n-4) +20*a(n-5) -a(n-6)

k=5: [order 7]

k=6: [order 9]

k=7: [order 9]

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 + 3*n + 1

n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 2*n + 1

n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 + 3*n + 1

n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 + 5*n^2 + 6*n - 1

n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 + 7*n^3 + 17*n^2 - n - 1

Example

Some solutions for n=6 k=4
..1. .0. .1. .0. .1. .4. .2. .2. .0. .0. .1. .2. .1. .0. .3. .2
..1. .4. .0. .3. .2. .2. .4. .1. .2. .2. .1. .4. .0. .1. .2. .0
..0. .4. .4. .2. .3. .1. .1. .4. .3. .2. .1. .0. .4. .3. .4. .0
..1. .2. .1. .0. .2. .3. .4. .3. .1. .2. .1. .4. .1. .4. .4. .1
..1. .0. .3. .3. .3. .4. .0. .1. .2. .4. .2. .3. .0. .2. .2. .2
..4. .2. .2. .4. .2. .0. .1. .3. .3. .1. .3. .0. .2. .0. .1. .0

Crossrefs

Column 1 is A019274(n+2).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A000578(n+1).

Sequence in context: A244832 A250351 A269690 * A269776 A269619 A269435

Adjacent sequences: A269491 A269492 A269493 * A269495 A269496 A269497

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 28 2016

Status

approved