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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 pseudopolynomial quasipolynomial with period 2

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

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

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

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R. H. Hardin, <a href="/A247726/b247726.txt">Table of n, a(n) for n = 1..9999</a>

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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

1,1

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

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 pseudopolynomial with period 2

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

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

n=5: [order 72]

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

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nonn,tabl

R. H. Hardin, Sep 23 2014

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