A250561 T(n,k)=Number of length n+2 0..k arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero

2, 5, 8, 8, 25, 14, 13, 60, 83, 32, 18, 117, 302, 297, 62, 25, 200, 761, 1516, 989, 128, 32, 321, 1648, 5105, 7126, 3113, 254, 41, 480, 3125, 13732, 31525, 30780, 9611, 512, 50, 681, 5446, 31173, 106362, 177421, 127586, 29257, 1022, 61, 940, 8843, 63400, 290909

Offset

1,1

Comments

Table starts

....2......5.......8........13.........18.........25..........32...........41

....8.....25......60.......117........200........321.........480..........681

...14.....83.....302.......761.......1648.......3125........5446.........8843

...32....297....1516......5105......13732......31173.......63400.......117749

...62....989....7126.....31525.....106362.....290909......695890......1486139

..128...3113...30780....177421.....744564....2457921.....6924692.....17094253

..254...9611..127586....937817....4808120...18934449....62245658....176612641

..512..29257..518052...4803653...29723864..137976845...522997696...1688068993

.1022..88503.2085808..24257725..180290280..980389815..4258085394..15526286669

.2048.266769.8367220.121800949.1085927844.6899647449.34261234132.140731044189

Links

R. H. Hardin, Table of n, a(n) for n = 1..159

Formula

Empirical for column k:

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

k=2: [order 10] for n>15

Empirical for row n:

n=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4); also a quadratic polynomial plus a constant quasipolynomial with period 2

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

n=3: [order 21; also a quartic polynomial plus a linear quasipolynomial with period 60]

Example

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

Crossrefs

Row 1 is A000982(n+1)

Row 2 is A250321

Sequence in context: A351391 A046825 A250320 * A131716 A011279 A185094

Adjacent sequences: A250558 A250559 A250560 * A250562 A250563 A250564

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 25 2014

Status

approved