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A245995 T(n,k)=Number of length n+2 0..k arrays with no pair in any consecutive three terms totalling exactly k 14

%I

%S 2,8,2,28,12,2,64,68,18,2,126,208,164,26,2,216,534,676,396,38,2,344,

%T 1116,2262,2196,956,56,2,512,2120,5766,9582,7132,2308,82,2,730,3648,

%U 13064,29790,40590,23168,5572,120,2,1000,5930,25992,80504,153906,171942,75260

%N T(n,k)=Number of length n+2 0..k arrays with no pair in any consecutive three terms totalling exactly k

%C Table starts

%C .2...8....28......64......126.......216........344.........512..........730

%C .2..12....68.....208......534......1116.......2120........3648.........5930

%C .2..18...164.....676.....2262......5766......13064.......25992........48170

%C .2..26...396....2196.....9582.....29790......80504......185192.......391290

%C .2..38...956....7132....40590....153906.....496088.....1319480......3178490

%C .2..56..2308...23168...171942....795144....3057032.....9401216.....25819210

%C .2..82..5572...75260...728358...4108062...18838280....66983128....209732170

%C .2.120.13452..244464..3085374..21223992..116086712...477250848...1703676570

%C .2.176.32476..794096.13069854.109652160..715358552..3400384160..13839144730

%C .2.258.78404.2579500.55364790.566509902.4408238024.24227537592.112416834410

%H R. H. Hardin, <a href="/A245995/b245995.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +a(n-3)

%F k=3: a(n) = 2*a(n-1) +a(n-2)

%F k=4: a(n) = 2*a(n-1) +a(n-2) +9*a(n-3) +3*a(n-4)

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

%F k=6: a(n) = 4*a(n-1) +a(n-2) +25*a(n-3) +5*a(n-4)

%F k=7: a(n) = 6*a(n-1) +a(n-2)

%F k=8: a(n) = 6*a(n-1) +a(n-2) +49*a(n-3) +7*a(n-4)

%F k=9: a(n) = 8*a(n-1) +a(n-2)

%F Empirical for row n:

%F n=1: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)

%F n=2: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7)

%F n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9)

%F n=4: [order 11]

%F n=5: [order 13]

%F n=6: [order 15]

%F n=7: [order 17]

%e Some solutions for n=5 k=4

%e ..3....0....4....0....0....4....2....1....0....1....1....3....4....1....3....2

%e ..3....0....3....0....2....1....3....2....3....4....4....3....4....1....4....4

%e ..3....3....2....0....0....2....3....0....0....4....4....4....3....0....2....4

%e ..3....2....3....0....1....0....2....1....3....2....4....3....4....0....4....4

%e ..2....4....0....2....0....3....0....0....2....1....3....4....2....1....3....4

%e ..4....4....3....0....1....3....1....2....0....0....4....2....1....0....2....4

%e ..1....1....0....0....2....2....1....3....0....2....3....4....1....1....0....3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Aug 09 2014

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)