A258894 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum

242, 900, 900, 3036, 2304, 3036, 10201, 4489, 4489, 10201, 30870, 10680, 6072, 10680, 30870, 94249, 23409, 8100, 8100, 23409, 94249, 271350, 51188, 12804, 7225, 12804, 51188, 271350, 786769, 104329, 20164, 9604, 9604, 20164, 104329, 786769, 2190720

Offset

1,1

Comments

Table starts

.....242....900...3036.10201.30870.94249.271350.786769.2190720.6135529.16733464

.....900...2304...4489.10680.23409.51188.104329.216395..430336..849760..1635841

....3036...4489...6072..8100.12804.20164..33252..54756...88312..141376...227568

...10201..10680...8100..7225..9604.13221..17424..23393...30276...39565....50176

...30870..23409..12804..9604.12544.16384..21320..27556...35360...44944....56680

...94249..51188..20164.13221.16384.21025..26244..33485...41616...52425....64516

..271350.104329..33252.17424.21320.26244..32400..40000...49288...60516....74000

..786769.216395..54756.23393.27556.33485..40000..48841...58564...71285....85264

.2190720.430336..88312.30276.35360.41616..49288..58564...69696...82944....98600

.6135529.849760.141376.39565.44944.52425..60516..71285...82944...97969...114244

Links

R. H. Hardin, Table of n, a(n) for n = 1..9378

Formula

Empirical for column k:

k=1: [linear recurrence of order 34]

k=2: [order 24] for n>27

k=3: [order 24] for n>27

k=4: 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) for n>11

k=5: 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) for n>11

k=6: 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) for n>11

k=7: 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) for n>11

Empirical quasipolynomials for column k:

k=4: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 2 for n>3

k=5: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 2 for n>3

k=6: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 2 for n>3

k=7: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 2 for n>3

Example

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

Crossrefs

Sequence in context: A094908 A205594 A070284 * A258887 A234484 A160551

Adjacent sequences: A258891 A258892 A258893 * A258895 A258896 A258897

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 14 2015

Status

approved