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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 16:24 EDT 2021. Contains 346273 sequences. (Running on oeis4.)