A250432 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column

16, 36, 36, 81, 108, 81, 144, 324, 324, 144, 256, 720, 1296, 720, 256, 400, 1600, 3600, 3600, 1600, 400, 625, 3000, 10000, 12000, 10000, 3000, 625, 900, 5625, 22500, 40000, 40000, 22500, 5625, 900, 1296, 9450, 50625, 105000, 160000, 105000, 50625, 9450

Offset

1,1

Comments

Table starts

...16....36.....81.....144......256.......400.......625........900........1296

...36...108....324.....720.....1600......3000......5625.......9450.......15876

...81...324...1296....3600....10000.....22500.....50625......99225......194481

..144...720...3600...12000....40000....105000....275625.....617400.....1382976

..256..1600..10000...40000...160000....490000...1500625....3841600.....9834496

..400..3000..22500..105000...490000...1715000...6002500...17287200....49787136

..625..5625..50625..275625..1500625...6002500..24010000...77792400...252047376

..900..9450..99225..617400..3841600..17287200..77792400..280052640..1008189504

.1296.15876.194481.1382976..9834496..49787136.252047376.1008189504..4032758016

.1764.24696.345744.2765952.22127616.124467840.700131600.3080579040.13554547776

Essentially the same as A202100; the mapping between the binary arrays in both sequences is by flipping all entries in one set of arrays. - Joerg Arndt, Dec 01 2014

Links

R. H. Hardin, Table of n, a(n) for n = 1..1104

Formula

Empirical for column k:

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

k=2: [order 12; also a polynomial of degree 6 plus a quasipolynomial of degree 4 with period 2]

k=3: [order 16; also a polynomial of degree 8 plus a quasipolynomial of degree 6 with period 2]

k=4: [order 20; also a polynomial of degree 10 plus a quasipolynomial of degree 8 with period 2]

k=5: [order 24; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 2]

k=6: [order 28; also a polynomial of degree 14 plus a quasipolynomial of degree 12 with period 2]

k=7: [order 32; also a polynomial of degree 16 plus a quasipolynomial of degree 14 with period 2]

Example

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

Crossrefs

Column 1 is A030179(n+3), A202093 - A202099 (further columns).

Sequence in context: A317818 A236463 A070588 * A183196 A109287 A294155

Adjacent sequences: A250429 A250430 A250431 * A250433 A250434 A250435

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2014

Status

approved