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A199530 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements 11

%I #5 Mar 31 2012 12:36:36

%S 1,1,2,1,4,6,1,6,18,12,1,8,36,72,32,1,10,60,212,320,80,1,12,90,464,

%T 1324,1414,200,1,14,126,860,3734,8342,6346,520,1,16,168,1432,8470,

%U 30484,53302,28766,1336,1,18,216,2212,16682,84852,252154,343710,131246,3472,1,20,270

%N T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements

%C Table starts

%C ....1......1........1.........1.........1..........1...........1...........1

%C ....2......4........6.........8........10.........12..........14..........16

%C ....6.....18.......36........60........90........126.........168.........216

%C ...12.....72......212.......464.......860.......1432........2212........3232

%C ...32....320.....1324......3734......8470......16682.......29750.......49284

%C ...80...1414.....8342.....30484.....84852.....197962......407946......766664

%C ..200...6346....53302....252154....860854....2378412.....5662636....12071420

%C ..520..28766...343710...2105064...8815392...28844590....79345982...191873280

%C .1336.131246..2232322..17701326..90927530..352355640..1119873360..3071898666

%C .3472.602390.14582218.149708146.943302430.4329146404.15897133212.49465959068

%H R. H. Hardin, <a href="/A199530/b199530.txt">Table of n, a(n) for n = 1..1096</a>

%F Empirical for rows:

%F T(1,k) = 1

%F T(2,k) = 2*k

%F T(3,k) = 3*k^2 + 3*k

%F T(4,k) = (16/3)*k^3 + 8*k^2 - (4/3)*k

%F T(5,k) = (115/12)*k^4 + (115/6)*k^3 + (41/12)*k^2 - (1/6)*k

%F T(6,k) = (88/5)*k^5 + 44*k^4 + (58/3)*k^3 - 3*k^2 + (31/15)*k

%F T(7,k) = (5887/180)*k^6 + (5887/60)*k^5 + (620/9)*k^4 + (11/12)*k^3 + (433/180)*k^2 - (91/30)*k

%e Some solutions for n=6 k=5

%e ..1...-1....0...-4...-1....4....1...-5....1....2...-1....1....3....3....1....5

%e ..0...-1...-1...-3....0....5...-3....0....1...-3...-3...-4....2...-5....1....2

%e .-4....5....3...-1...-2...-3....5....1...-1....5....0....2...-3....4...-4...-5

%e ..3...-2...-3....2....2...-4...-1....2...-4....4...-2....2....2...-5....5...-1

%e ..1...-3...-2....4...-4...-4....0....5....2...-5....5....4...-4....0...-2....1

%e .-1....2....3....2....5....2...-2...-3....1...-3....1...-5....0....3...-1...-2

%Y Column 1 is A102881

%Y Row 3 is A028896

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Nov 07 2011

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)