A247726 T(n,k)=Number of length n+3 0..k arrays with no disjoint pairs in any consecutive four terms having the same sum

8, 48, 8, 168, 90, 8, 440, 456, 172, 8, 960, 1592, 1248, 334, 8, 1848, 4344, 5796, 3424, 656, 8, 3248, 10098, 19744, 21152, 9392, 1300, 8, 5328, 20816, 55372, 89836, 77236, 25822, 2584, 8, 8280, 39264, 133780, 303924, 408644, 282384, 71060, 5148, 8, 12320

Offset

1,1

Comments

Table starts

.8....48.....168......440.......960.......1848........3248.........5328

.8....90.....456.....1592......4344......10098.......20816........39264

.8...172....1248.....5796.....19744......55372......133780.......290004

.8...334....3424....21152.....89836.....303924......860360......2143214

.8...656....9392....77236....408644....1668072.....5532212.....15837692

.8..1300...25822...282384...1859736....9157806....35577396....117045466

.8..2584...71060..1032952...8465936...50284864...228817500....865051288

.8..5148..195536..3779018..38539276..276119316..1471661464...6393427268

.8.10272..537880.13825712.175434372.1516191100..9465023576..47252411120

.8.20520.1480026.50587924.798617096.8325624724.60874728614.349232818280

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 2*a(n-1) +2*a(n-4) -4*a(n-5)

k=3: [order 27]

k=4: [order 45]

k=5: [order 76]

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8); also a polynomial of degree 5 plus a linear quasipolynomial with period 2

n=3: [order 16; also a polynomial of degree 6 plus a quadratic quasipolynomial with period 12]

n=4: [order 34; also a polynomial of degree 7 plus a cubic quasipolynomial with period 420]

n=5: [order 72]

Example

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

Crossrefs

Sequence in context: A034349 A296797 A024108 * A263506 A216323 A335351

Adjacent sequences: A247723 A247724 A247725 * A247727 A247728 A247729

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 23 2014

Status

approved