A102881 -id:A102881 - cp's OEIS frontend

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.

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, 1324, 1414, 200, 1, 14, 126, 860, 3734, 8342, 6346, 520, 1, 16, 168, 1432, 8470, 30484, 53302, 28766, 1336, 1, 18, 216, 2212, 16682, 84852, 252154, 343710, 131246, 3472, 1, 20, 270

Offset: 1

R. H. Hardin Nov 07 2011

Table starts
....1......1........1.........1.........1..........1...........1...........1
....2......4........6.........8........10.........12..........14..........16
....6.....18.......36........60........90........126.........168.........216
...12.....72......212.......464.......860.......1432........2212........3232
...32....320.....1324......3734......8470......16682.......29750.......49284
...80...1414.....8342.....30484.....84852.....197962......407946......766664
..200...6346....53302....252154....860854....2378412.....5662636....12071420
..520..28766...343710...2105064...8815392...28844590....79345982...191873280
.1336.131246..2232322..17701326..90927530..352355640..1119873360..3071898666
.3472.602390.14582218.149708146.943302430.4329146404.15897133212.49465959068

			Some solutions for n=6 k=5
..1...-1....0...-4...-1....4....1...-5....1....2...-1....1....3....3....1....5
..0...-1...-1...-3....0....5...-3....0....1...-3...-3...-4....2...-5....1....2
.-4....5....3...-1...-2...-3....5....1...-1....5....0....2...-3....4...-4...-5
..3...-2...-3....2....2...-4...-1....2...-4....4...-2....2....2...-5....5...-1
..1...-3...-2....4...-4...-4....0....5....2...-5....5....4...-4....0...-2....1
.-1....2....3....2....5....2...-2...-3....1...-3....1...-5....0....3...-1...-2

R. H. Hardin, Table of n, a(n) for n = 1..1096

Column 1 is A102881

Row 3 is A028896

Empirical for rows:
T(1,k) = 1
T(2,k) = 2*k
T(3,k) = 3*k^2 + 3*k
T(4,k) = (16/3)*k^3 + 8*k^2 - (4/3)*k
T(5,k) = (115/12)*k^4 + (115/6)*k^3 + (41/12)*k^2 - (1/6)*k
T(6,k) = (88/5)*k^5 + 44*k^4 + (58/3)*k^3 - 3*k^2 + (31/15)*k
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

A102882 Expansion of (1+2x)/sqrt((1-3x^2)(1+4x+5x^2)).

Original entry on oeis.org

1, 0, 1, 2, -3, 16, -27, 66, -79, 96, 129, -686, 2429, -5520, 11125, -15438, 10785, 36032, -182591, 556194, -1279171, 2393296, -3187131, 1157666, 10934481, -48082656, 136730689, -304493326, 539172285, -647406800, -53647147, 3352290450, -12929496767, 34720868736, -74092036479

Offset: 0

Paul Barry, Jan 15 2005

Binomial transform is A102881.

CoefficientList[Series[(1+2*x)/Sqrt[1+4*x+2*x^2-12*x^3-15*x^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)

G.f.: (1+2x)/sqrt(1+4x+2x^2-12x^3-15x^4).
Conjecture: n*(n+1)*a(n) +2*(2*n+3)*(n-1)*a(n-1) +2*(n^2-7)*a(n-2) +6*(5+n-2*n^2)*a(n-3) -15*(n+2)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 09 2012
Lim sup n->infinity |a(n)|^(1/n) = sqrt(5). - Vaclav Kotesovec, Feb 03 2014

cp's OEIS Frontend

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.

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